ENGLISH

Global Surgery Formula for the Casson-Walker Invariant.

By Christine Lescop

Book information

Publisher
Princeton University Press
Year
1995
ISBN
0691021325
Language
english
Format
DJVU
Filesize
4 MB (4369283 bytes)
Series
Annals of Mathematics Studies-140
Pages
150\151
Time added
2011-04-28 18:43:47

Description

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.

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