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

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Lescop, Christine,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2014]; ©1996
• Year of Publication: 2014
• Language: English
• Series: Annals of Mathematics Studies ; 140
• Physical Description: 1 online resource (150 p.)
• Other title: Frontmatter --; Table of contents --; Chapter 1. Introduction and statements of the results --; Chapter 2. The Alexander series of a link in a rational homology sphere and some of its properties --; Chapter 3. Invariance of the surgery formula under a twist homeomorphism --; Chapter 4. The formula for surgeries starting from rational homology spheres --; Chapter 5. The invariant A. for 3-manifolds with nonzero rank --; Chapter 6. Applications and variants of the surgery formula --; Appendix. More about the Alexander series --; Bibliography --; Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400865154; 9783110494914; 9783110442496
• DOI: 10.1515/9781400865154
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Christine Lescop.

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.