Lectures on the topology of 3manifolds : an introduction to the Casson invariant
 Author/Creator
 Saveliev, Nikolai, 1966
 Language
 English.
 Edition
 2nd rev. ed.
 Imprint
 Berlin ; Boston : De Gruyter, c2012.
 Physical description
 xi, 207 p. : ill ; 24 cm.
Access
Available online

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QA613.2 .S28 2012

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QA613.2 .S28 2012
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Contents/Summary
 Bibliography
 Includes bibliographical references (p.[195]203) and index.
 Contents

 Preface Introduction Glossary 1 Heegaard splittings 1.1 Introduction 1.2 Existence of Heegaard splittings 1.3 Stable equivalence of Heegaard splittings 1.4 The mapping class group 1.5 Manifolds of Heegaard genus 1 1.6 Seifert manifolds 1.7 Heegaard diagrams 2 Dehn surgery 2.1 Knots and links in 3manifolds 2.2 Surgery on links in S3 2.3 Surgery description of lens spaces and Seifert manifolds 2.4 Surgery and 4manifolds 3 Kirby calculus 3.1 The linking number 3.2 Kirby moves 3.3 The linking matrix 3.4 Reversing orientation 4 Even surgeries 5 Review of 4manifolds 5.1 Definition of the intersection form 5.2 The unimodular integral forms 5.3 Fourmanifolds and intersection forms 6 Fourmanifolds with boundary 6.1 The intersection form 6.2 Homology spheres via surgery on knots 6.3 Seifert homology spheres 6.4 The Rohlin invariant 7 Invariants of knots and links 7.1 Seifert surfaces 7.2 Seifert matrices 7.3 The Alexander polynomial 7.4 Other invariants from Seifert surfaces 7.5 Knots in homology spheres 7.6 Boundary links and the Alexander polynomial 8 Fibered knots 8.1 The definition of a fibered knot 8.2 The monodromy 8.3 More about torus knots 8.4 Joins 8.5 The monodromy of torus knots 8.6 Open book decompositions 9 The Arfinvariant 9.1 The Arfinvariant of a quadratic form 9.2 The Arfinvariant of a knot 10 Rohlin.
 (source: Nielsen Book Data)
 Publisher's Summary
 This textbook now in its second revised and extended edition introduces the topology of 3 and 4dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Threemanifolds (Topology)
Bibliographic information
 Publication date
 2012
 Responsibility
 Nikolai Saveliev.
 Title Variation
 Lecture on the topology of three manifolds
 ISBN
 9783110250350
 3110250357
 9783110250367
 3110250365