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Record Nr. |
UNINA9910827210603321 |
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Autore |
Lescop Christine <1966-> |
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Titolo |
Global surgery formula for the Casson-Walker invariant / / by Christine Lescop |
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Pubbl/distr/stampa |
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Princeton, New Jersey : , : Princeton University Press, , 1996 |
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©1996 |
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ISBN |
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0-691-02133-3 |
1-4008-6515-8 |
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Descrizione fisica |
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1 online resource (156 p.) |
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Collana |
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Annals of Mathematics Studies ; ; Number 10 |
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Disciplina |
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Soggetti |
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Surgery (Topology) |
Three-manifolds (Topology) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Front matter -- 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 |
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Sommario/riassunto |
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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 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. |
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