Tu, Loring W.
Overview
Works:  9 works in 105 publications in 5 languages and 2,259 library holdings 

Roles:  Author 
Classifications:  QA613.6, 514.72 
Publication Timeline
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Most widely held works by
Loring W Tu
Differential forms in algebraic topology by
Raoul Bott(
Book
)
35 editions published between 1981 and 2010 in 5 languages and held by 730 WorldCat member libraries worldwide
This text, developed from a firstyear graduate course in algebraic topology, is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas de Rham theory, the Cechde Rham complex, spectral sequences, and characteristic classesand include some applications to homotopy theory. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, "Differential Forms in Algebraic Topology" should be suitable for selfstudy or for a one semester course in topology
35 editions published between 1981 and 2010 in 5 languages and held by 730 WorldCat member libraries worldwide
This text, developed from a firstyear graduate course in algebraic topology, is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas de Rham theory, the Cechde Rham complex, spectral sequences, and characteristic classesand include some applications to homotopy theory. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, "Differential Forms in Algebraic Topology" should be suitable for selfstudy or for a one semester course in topology
An introduction to manifolds by
Loring W Tu(
Book
)
43 editions published between 2007 and 2011 in English and held by 421 WorldCat member libraries worldwide
Manifolds, the higherdimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite pointset topology is included in an appendix of twenty pages other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a onesemester graduate or advanced undergraduate course, as well as by students engaged in selfstudy. Requiring only minimal undergraduate prerequisites, Introduction to Manifolds is also an excellent foundation for Springer GTM 82, Differential Forms in Algebraic Topology (by Raoul Bott and Loring W. Tu)
43 editions published between 2007 and 2011 in English and held by 421 WorldCat member libraries worldwide
Manifolds, the higherdimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite pointset topology is included in an appendix of twenty pages other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a onesemester graduate or advanced undergraduate course, as well as by students engaged in selfstudy. Requiring only minimal undergraduate prerequisites, Introduction to Manifolds is also an excellent foundation for Springer GTM 82, Differential Forms in Algebraic Topology (by Raoul Bott and Loring W. Tu)
Hodge theory and the local Torelli problem by
Loring W Tu(
Book
)
11 editions published in 1983 in English and held by 222 WorldCat member libraries worldwide
11 editions published in 1983 in English and held by 222 WorldCat member libraries worldwide
Differencialʹnye formy v algebraičeskoj topologii by
Raoul Bott(
Book
)
5 editions published in 1989 in Russian and held by 11 WorldCat member libraries worldwide
5 editions published in 1989 in Russian and held by 11 WorldCat member libraries worldwide
DIFFERENTIAL GEOMETRY by
Loring W Tu(
Book
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
An introduction to manifolds (9780387480985) by
Loring W Tu(
Book
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
Hodge theory and the local Torelli problem by
Loring W Tu(
Book
)
2 editions published in 1983 in English and held by 1 WorldCat member library worldwide
2 editions published in 1983 in English and held by 1 WorldCat member library worldwide
Variation of Hodge structure and the local Torelli problem by
Loring W Tu(
Book
)
1 edition published in 1979 in English and held by 1 WorldCat member library worldwide
1 edition published in 1979 in English and held by 1 WorldCat member library worldwide
Differential Forms in Algebraic Topology by
Raoul Bott(
)
in Undetermined and held by 0 WorldCat member libraries worldwide
in Undetermined and held by 0 WorldCat member libraries worldwide
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