| Description |
1 online resource (155 pages) : illustrations |
| Series |
Annals of Mathematics Studies ; Number 10 |
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Annals of mathematics studies ; no. 10.
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| Contents |
880-01 Cover; Title; Copyright; Table of contents; Chapter 1: Introduction and statements of the results; 1.1 Introduction; 1.2 Conventions; 1.3 Surgery presentations and associated functions; 1.4 Introduction of the surgery formula F; 1.5 Statement of the theorem; 1.6 Sketch of the proof of the theorem and organization of the book; 1.7 Equivalent definitions for F; Chapter 2: The Alexander series of a link in a rational homology sphere and some of its properties; 2.1 The background; 2.2 A definition of the Alexander series; 2.3 A list of properties for the Alexander series |
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880-01/(S 2.4 Functions of the linking numbers of a link2.5 The first terms of the Alexander series; Chapter 3: Invariance of the surgery formula under a twist homeomorphism; 3.1 Introduction; 3.2 Variation of the different pieces of FM under an ω-twist: the statements; 3.3 Proofs of 3.2.13 and 3.2.16; 3.4 More linking functions: semi-open graphs and functions α; 3.5 Variation of the ζ-coefficients under an ω-twist; 3.6 Proof of 3.2.11 (variation of the piece containing the ζ-coefficients under the ω-twist); Chapter 4: The formula for surgeries starting from rational homology spheres |
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880-02 6.2 The formula involving the figure-eight linking6.3 Congruences and relations with the Rohlin invariant; 6.4 The surgery formula in terms of one-variable Alexander polynomials; Appendix: More about the Alexander series; A.1 Introduction; A.2 Complete definition of the Reidemeister torsion of (N, o(N)) up to positive units; A.3 Proof of the symmetry property of the Reidemeister torsion; A.4 Various properties of the Reidemeister torsion; A.5 A systematic way of computing the Alexander polynomials of links in Ŝ3; A.6 Relations with one-variable Alexander polynomials; Bibliography |
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880-02/(S 4.1 Introduction4.2 Sketch of the proof of Proposition T2; 4.3 Proof of Lemma 4.2.2; 4.4 Proof of Lemma 4.2.3; 4.5 Proof of Lemma 4.2.5; 4.6 The Walker surgery formula; 4.7 Comparing T2 with the Walker surgery formula; Chapter 5: The invariant λ for 3-manifolds with nonzero rank; 5.1 Introduction; 5.2 The coefficients a1 of homology unlinks in rational homology spheres (after Hoste); 5.3 Computing λ for manifolds with rank at least 2; Chapter 6: Applications and variants of the surgery formula; 6.1 Computing λ for all oriented Seifert fibered spaces using the formula |
| Summary |
This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S 3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S 3 is described, and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, l is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Surgery (Topology)
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Three-manifolds (Topology)
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Surgery (Topology)
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Three-manifolds (Topology)
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| Form |
Electronic book
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| ISBN |
9781400865154 |
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1400865158 |
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