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Global Surgery Formula for the Casson-Walker Invariant
Author: Christine Lescop

ISBN: 9780691021324
Format: Paperback
Number Of Pages: 150
Published: 16 November 1995
Country of Publication: US
Dimensions (cm): 22.9 x 15.2 x 0.8
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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