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

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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.

Author Biography:

Christine Lescop is Researcher in Mathematics at the Centre National de la Recherche Scientifique at the Institut Fourier in Grenoble, France.
Release date Australia
January 11th, 1996
Audiences
  • Professional & Vocational
  • Tertiary Education (US: College)
Pages
150
Dimensions
152x229x8
ISBN-13
9780691021324
Product ID
2800867

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