Saveliev, Nikolai 1966
Overview
Works:  4 works in 15 publications in 2 languages and 650 library holdings 

Roles:  Author 
Classifications:  QA613.2, 514.34 
Publication Timeline
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Most widely held works by
Nikolai Saveliev
Lectures on the Topology of 3Manifolds an Introduction to the Casson Invariant
by
Nikolai Saveliev(
Book
)
10 editions published between 1999 and 2012 in English and German and held by 424 WorldCat member libraries worldwide
"Progress in lowdimensional topology has been very fast in the last two decades, leading to the solutions of many difficult problems." "Among the highlights of this period are Casson's results on the Rohlin invariant of homotopy 3spheres, as well as his [lambda]invariant. The purpose of this book is to provide a muchneeded bridge to these modern topics. The book covers some classical topics, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and gives a brief sketch of links with the latest developments in lowdimensional topology and gauge theory." "The text will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincare duality on manifolds."BOOK JACKET
10 editions published between 1999 and 2012 in English and German and held by 424 WorldCat member libraries worldwide
"Progress in lowdimensional topology has been very fast in the last two decades, leading to the solutions of many difficult problems." "Among the highlights of this period are Casson's results on the Rohlin invariant of homotopy 3spheres, as well as his [lambda]invariant. The purpose of this book is to provide a muchneeded bridge to these modern topics. The book covers some classical topics, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and gives a brief sketch of links with the latest developments in lowdimensional topology and gauge theory." "The text will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincare duality on manifolds."BOOK JACKET
Invariants for homology 3spheres
by
Nikolai Saveliev(
Book
)
1 edition published in 2002 in English and held by 219 WorldCat member libraries worldwide
Homology 3sphere is a closed 3dimensional manifold whose homology equals that of the 3sphere. These objects may look rather special but they have played an outstanding role in geometric topology for the past fifty years. The book gives a systematic exposition of diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered in the book are constructions and classification of homology 3spheres, Rokhlin invariant, Casson invariant and its numerous extensions, including invariants of Walker and Lescop, Herald and Lin invariants of knots, and equivariant Casson invariants, followed by Floer homology and gaugetheoretical invariants of homology cobordism. Many of the topics covered in the book appear in monograph form for the first time. The book gives a rather broad overview of ideas and methods and provides a comprehensive bibliography. It will be appealing to both graduate students and researchers in mathematics and theoretical physics
1 edition published in 2002 in English and held by 219 WorldCat member libraries worldwide
Homology 3sphere is a closed 3dimensional manifold whose homology equals that of the 3sphere. These objects may look rather special but they have played an outstanding role in geometric topology for the past fifty years. The book gives a systematic exposition of diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered in the book are constructions and classification of homology 3spheres, Rokhlin invariant, Casson invariant and its numerous extensions, including invariants of Walker and Lescop, Herald and Lin invariants of knots, and equivariant Casson invariants, followed by Floer homology and gaugetheoretical invariants of homology cobordism. Many of the topics covered in the book appear in monograph form for the first time. The book gives a rather broad overview of ideas and methods and provides a comprehensive bibliography. It will be appealing to both graduate students and researchers in mathematics and theoretical physics
Invariants of Homology 3Spheres
by
Nikolai Saveliev(
Book
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
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