Naber, Gregory L. 1948
Overview
Works:  31 works in 237 publications in 1 language and 4,485 library holdings 

Genres:  Encyclopedias Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA1, 514 
Publication Timeline
.
Most widely held works by
Gregory L Naber
The geometry of Minkowski spacetime : an introduction to the mathematics of the special theory of relativity by
Gregory L Naber(
Book
)
43 editions published between 1992 and 2014 in English and held by 760 WorldCat member libraries worldwide
This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman's characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrovtype classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac's famous Scissors Problem and its relation to the notion of a twovalued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presence of gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary pointset topology. The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title. Reviews of first edition: "... a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics." (American Mathematical Society, 1993) "Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations." (CHOICE, 1993) "... his talent in choosing the most significant results and ordering them within the book can't be denied. The reading of the book is, really, a pleasure." (Dutch Mathematical Society, 1993)
43 editions published between 1992 and 2014 in English and held by 760 WorldCat member libraries worldwide
This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman's characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrovtype classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac's famous Scissors Problem and its relation to the notion of a twovalued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presence of gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary pointset topology. The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title. Reviews of first edition: "... a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics." (American Mathematical Society, 1993) "Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations." (CHOICE, 1993) "... his talent in choosing the most significant results and ordering them within the book can't be denied. The reading of the book is, really, a pleasure." (Dutch Mathematical Society, 1993)
Topological methods in Euclidean spaces by
Gregory L Naber(
Book
)
19 editions published between 1980 and 2012 in English and Undetermined and held by 539 WorldCat member libraries worldwide
9 The Brouwer Fixed Point Theorem10 Topological dimension of compact subsets of Rn; Supplementary exercises; Chapter 3 Homotopy theory and the fundamental group; 1 Introduction; 2 The homotopy relation, nullhomotopic maps, and contractible spaces; 3 Maps of spheres; 4 The fundamental group; 5 Fundamental groups of the spheres; Supplementary exercises; Chapter 4 Simplicial homology theory; 1 Introduction; 2 Oriented complexes and chains; 3 Boundary operators; 4 Cycles, boundaries, and homology groups; 5 Elementary examples
19 editions published between 1980 and 2012 in English and Undetermined and held by 539 WorldCat member libraries worldwide
9 The Brouwer Fixed Point Theorem10 Topological dimension of compact subsets of Rn; Supplementary exercises; Chapter 3 Homotopy theory and the fundamental group; 1 Introduction; 2 The homotopy relation, nullhomotopic maps, and contractible spaces; 3 Maps of spheres; 4 The fundamental group; 5 Fundamental groups of the spheres; Supplementary exercises; Chapter 4 Simplicial homology theory; 1 Introduction; 2 Oriented complexes and chains; 3 Boundary operators; 4 Cycles, boundaries, and homology groups; 5 Elementary examples
Topology, geometry, and gauge fields : foundations by
Gregory L Naber(
Book
)
32 editions published between 1997 and 2014 in English and held by 523 WorldCat member libraries worldwide
This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The author's point of view is that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The goal is to weave together rudimentary notions from the classical gauge theory of physicists with the topological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, and a solid background in real analysis and linear algebra with some of the vocabulary of modern algebra. To such a reader we offer an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of antiselfdual SU(2) connections on S[subscript 4] with instanton number 1
32 editions published between 1997 and 2014 in English and held by 523 WorldCat member libraries worldwide
This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The author's point of view is that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The goal is to weave together rudimentary notions from the classical gauge theory of physicists with the topological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, and a solid background in real analysis and linear algebra with some of the vocabulary of modern algebra. To such a reader we offer an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of antiselfdual SU(2) connections on S[subscript 4] with instanton number 1
Spacetime and singularities : an introduction by
Gregory L Naber(
Book
)
24 editions published between 1988 and 2003 in English and held by 474 WorldCat member libraries worldwide
24 editions published between 1988 and 2003 in English and held by 474 WorldCat member libraries worldwide
Topology, geometry, and gauge fields : interactions by
Gregory L Naber(
Book
)
30 editions published between 2000 and 2011 in English and Undetermined and held by 431 WorldCat member libraries worldwide
This book covers topology and geometry beginning with an accessible account of the extraordinary and rather mysterious impact of mathematical physics, especially gauge theory, on the study of the geometry and topology of manifolds. Much of the mathematics developed in the book to study the classical field theories of physics (de Rham cohomology, Chern classes, SemiRiemannian manifolds, Cech cohomology, spinors etc.) is standard, but the treatment always keeps one eye on the physics and unhesitatingly sacrifices generality to clarity. The author brings the reader up to the level needed to conclude with a brief discussion of the SeibergWitten invariants. Although this volume can be read independently Naber carries on the program initiated in his earlier volume, Topology, Geometry and Gauge Fields: Foundations, Springer, 1997, and writes in much the same spirit with precisely the same philosophical motivation. A large number of exercises are included to encourage active participation on the part of the reader. This work will be of great interest to researchers and graduate students in the field of mathematical physics. REVIEWS OF TOPOLOGY, GEOMETRY, AND GAUGE FIELDS: FOUNDATIONS "It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics ... Naber combines a knowledge of his subject with an excellent informal writing style." NZMS NEWSLETTER " ... this book should be very interesting for mathematicians and
30 editions published between 2000 and 2011 in English and Undetermined and held by 431 WorldCat member libraries worldwide
This book covers topology and geometry beginning with an accessible account of the extraordinary and rather mysterious impact of mathematical physics, especially gauge theory, on the study of the geometry and topology of manifolds. Much of the mathematics developed in the book to study the classical field theories of physics (de Rham cohomology, Chern classes, SemiRiemannian manifolds, Cech cohomology, spinors etc.) is standard, but the treatment always keeps one eye on the physics and unhesitatingly sacrifices generality to clarity. The author brings the reader up to the level needed to conclude with a brief discussion of the SeibergWitten invariants. Although this volume can be read independently Naber carries on the program initiated in his earlier volume, Topology, Geometry and Gauge Fields: Foundations, Springer, 1997, and writes in much the same spirit with precisely the same philosophical motivation. A large number of exercises are included to encourage active participation on the part of the reader. This work will be of great interest to researchers and graduate students in the field of mathematical physics. REVIEWS OF TOPOLOGY, GEOMETRY, AND GAUGE FIELDS: FOUNDATIONS "It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics ... Naber combines a knowledge of his subject with an excellent informal writing style." NZMS NEWSLETTER " ... this book should be very interesting for mathematicians and
Encyclopedia of mathematical physics(
Book
)
16 editions published in 2006 in English and held by 185 WorldCat member libraries worldwide
The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their coursework. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originating from work in mathematical physics by providing them with focused high quality background information. Editorial Board: JeanPierre Fraṅoise, Universiť Pierre et Marie Curie, Paris, France Gregory L. Naber, Drexel University, Philadelphia, PA, USA Tsou Sheung Tsun, University of Oxford, UK Also available online via ScienceDirect (2006)  featuring extensive browsing, searching, and internal crossreferencing between articles in the work, plus dynamic linking to journal articles and abstract databases, making navigation flexible and easy
16 editions published in 2006 in English and held by 185 WorldCat member libraries worldwide
The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their coursework. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originating from work in mathematical physics by providing them with focused high quality background information. Editorial Board: JeanPierre Fraṅoise, Universiť Pierre et Marie Curie, Paris, France Gregory L. Naber, Drexel University, Philadelphia, PA, USA Tsou Sheung Tsun, University of Oxford, UK Also available online via ScienceDirect (2006)  featuring extensive browsing, searching, and internal crossreferencing between articles in the work, plus dynamic linking to journal articles and abstract databases, making navigation flexible and easy
Settheoretic topology : with emphasis on problems from the theory of coverings, zero dimensionality and cardinal invariants by
Gregory L Naber(
Book
)
10 editions published in 1977 in English and Undetermined and held by 85 WorldCat member libraries worldwide
10 editions published in 1977 in English and Undetermined and held by 85 WorldCat member libraries worldwide
Geometry, integrability and quantization : proceedings of ... International Conference ... Varna, Bulgaria by Integrability and Quantization International Conference Geometry(
)
in English and held by 14 WorldCat member libraries worldwide
in English and held by 14 WorldCat member libraries worldwide
Geometry, integrability and quantization by
Integrability and Quantitatization International Conference Geometry(
Book
)
7 editions published between 1999 and 2003 in English and held by 14 WorldCat member libraries worldwide
7 editions published between 1999 and 2003 in English and held by 14 WorldCat member libraries worldwide
Encyclopedia of mathematical physics. Shu xue wu li xue bai ke quan shu(
Book
)
12 editions published between 2006 and 2008 in English and held by 12 WorldCat member libraries worldwide
12 editions published between 2006 and 2008 in English and held by 12 WorldCat member libraries worldwide
Topology, Geometry and Gauge fields : Foundations by
Gregory L Naber(
)
3 editions published between 1997 and 2011 in English and held by 11 WorldCat member libraries worldwide
3 editions published between 1997 and 2011 in English and held by 11 WorldCat member libraries worldwide
Encyclopedia of mathematical physics(
Book
)
4 editions published in 2006 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 2006 in English and held by 4 WorldCat member libraries worldwide
Proceedings of Fourth International Conference Geometry, Integrability and Quantization : June 615, 2002, Sts. Constantine
and Elena, Bulgaria by
Integrability and Quantitatization International Conference Geometry(
Book
)
2 editions published in 2003 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2003 in English and held by 4 WorldCat member libraries worldwide
Encyclopedia of mathematical physics. Shu xue wu li xue bai ke quan shu(
Book
)
3 editions published in 2008 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 2008 in English and held by 4 WorldCat member libraries worldwide
Proceedings of Second International Conference Geometry, Integrability and Quantization : June 7  15, 2000, Sts. Constantine
and Elena, Bulgaria [near Varna] by
Integrability and Quantitatization International Conference Geometry(
Book
)
2 editions published in 2001 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2001 in English and held by 2 WorldCat member libraries worldwide
Encyclopedia of mathematical physics(
Book
)
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
Geometry, Integrability and Quantization, September 110, 1999 Sts. Constantine and Elena, Bulgaria by Integrability and Quantization International Conference Geometry(
Book
)
1 edition published in 1999 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1999 in English and held by 2 WorldCat member libraries worldwide
Encyclopedia of mathematical physics. Shu xue wu li xue bai ke quan shu(
Book
)
2 editions published in 2008 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2008 in English and held by 2 WorldCat member libraries worldwide
Encyclopedia of mathematical physics(
Book
)
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
Encyclopedia of mathematical physics(
Book
)
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
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Related Identities
 Tsou, S. T. (Sheung Tsun) Editor
 Françoise, J.P (JeanPierre) 1953 Author Editor
 Memphis State University Department of Mathematical Sciences
 Mladenov, I. M. (Ivailo M.)
 Bŭlgarska akademii︠a︡ na naukite
 California State University, Chico
 European Mathematical Society
 SpringerLink (Service en ligne)
 (JeanPierre) 1953
 Mladenov, Ivaïla. M.
Associated Subjects
Cell aggregationMathematics Combinatorial analysis Complex manifolds Difference equations Differentiable dynamical systems Dynamics Fluid dynamics Functions of complex variables Gauge fields (Physics) Generalized spaces General relativity (Physics) General relativity (Physics)Mathematics Geometric quantization Geometry Geometry, Algebraic Geometry, Differential Gravitation Integral geometry Lowdimensional topology Manifolds (Mathematics) Mathematical physics Mathematics Mechanics, Analytic Minkowski geometry Noncommutative rings Orderdisorder models Physics Quantum gravity Quantum theory Relativity (Physics) Set theory Singularities (Mathematics) Space and time Special relativity (Physics)Mathematics Statistical mechanics String models Topology
Alternative Names
Naber, Gregory
Naber, Gregory 1948
Naber, Gregory L.
Naber, Gregory Lawrence 1948
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