Global surgery formula for the Casson-Walker invariant / by Christine Lescop.

Format:

Book

Author/Creator:

Lescop, Christine, 1966- author.

Series:

Annals of mathematics studies ; Number 10.

Annals of Mathematics Studies ; Number 10

Language:

English

Subjects (All):

Surgery (Topology).

Three-manifolds (Topology).

Physical Description:

1 online resource (156 p.)

Edition:

1st ed.

Place of Publication:

Princeton, New Jersey : Princeton University Press, 1996.

Language Note:

English

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 topology. l becomes simpler as the first Betti number increases. As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of l under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.

Contents:

Front matter

Table of contents

Chapter 1. Introduction and statements of the results

Chapter 2. The Alexander series of a link in a rational homology sphere and some of its properties

Chapter 3. Invariance of the surgery formula under a twist homeomorphism

Chapter 4. The formula for surgeries starting from rational homology spheres

Chapter 5. The invariant A. for 3-manifolds with nonzero rank

Chapter 6. Applications and variants of the surgery formula

Appendix. More about the Alexander series

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-691-02133-3

1-4008-6515-8

OCLC:

888743940