Global surgery formula for the Casson-Walker invariant /
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 con...
Clasificación: | Libro Electrónico |
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Autor principal: | |
Formato: | Electrónico eBook |
Idioma: | Inglés |
Publicado: |
Princeton :
Princeton University Press,
1996.
|
Colección: | Annals of mathematics studies ;
no. 140. |
Temas: | |
Acceso en línea: | Texto completo |
Sumario: | 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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Descripción Física: | 1 online resource (150 pages) : illustrations |
Bibliografía: | Includes bibliographical references (pages 147-148) and index. |
ISBN: | 9781400865154 1400865158 |