Global Surgery Formula for the Casson-Walker Invariant. (AM-140)
Christine Lescop

Paper | 1995 | $46.95 / £27.95
150 pp. | 6 x 9

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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 S³. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S³ 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.

Table of Contents:

Ch. 1	Introduction and statements of the results	5
Ch. 2	The Alexander series of a link in a rational homology sphere and some of its properties	21
Ch. 3	Invariance of the surgery formula under a twist homeomorphism	35
Ch. 4	The formula for surgeries starting from rational homology spheres	60
Ch. 5	The invariant [lambda] for 3-manifolds with nonzero rank	81
Ch. 6	Applications and variants of the surgery formula	95
	Appendix: More about the Alexander series	117
	Bibliography	147
	Index	149

Series:

• Annals of Mathematics Studies
  Phillip A. Griffiths, John N. Mather, and Elias M. Stein, Editors

Subject Area:

• Mathematics

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For customers in the U.S., Canada, Latin America, Asia, and Australia
Paper: $46.95 ISBN13: 978-0-691-02132-4

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Paper: £27.95 ISBN13: 978-0-691-02132-4

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