An Extension of Casson's Invariant. (AM-126), Volume 126 / Kevin Walker.

Format:

Book

Author/Creator:

Walker, Kevin, author.

Series:

Annals of mathematics studies ; no. 126.

Annals of Mathematics Studies ; 308

Language:

English

Subjects (All):

Three-manifolds (Topology).

Invariants.

Physical Description:

1 online resource (140 pages) : illustrations.

Other Title:

Casson's invariant.

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

In English.

Summary:

This book describes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case. Let R(X) denote the space of conjugacy classes of representations of p(X) into SU(2). Let (W,W,F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is declared to be an appropriately defined intersection number of R(W) and R(W) inside R(F). The definition of this intersection number is a delicate task, as the spaces involved have singularities. A formula describing how l transforms under Dehn surgery is proved. The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of l. It is also shown that when M is a Z-homology sphere, l(M) determines the Rochlin invariant of M.

Contents:

Frontmatter

Contents

0. Introduction

1. Topology of Representation Spaces

2. Definition of λ

3. Various Properties of λ

4. The Dehn Surgery Formula

5. Combinatorial Definition of λ

6. Consequences of the Dehn Surgery Formula

A. Dedekind Sums

B. Alexander Polynomials

Bibliography

Notes:

Includes bibliographical references.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400882465

140088246X

OCLC:

979743249