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...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton :
Princeton University Press,
1996.
|
| Schriftenreihe: | Annals of mathematics studies ;
no. 140. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (150 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 147-148) and index. |
| ISBN: | 9781400865154 1400865158 |
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| 245 | 1 | 0 | |a Global surgery formula for the Casson-Walker invariant / |c by Christine Lescop. |
| 264 | 1 | |a Princeton : |b Princeton University Press, |c 1996. | |
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| 490 | 1 | |a Annals of mathematics studies ; |v number 140 | |
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| 505 | 0 | |a Ch. 1. Introduction and statements of the results -- Ch. 2. The Alexander series of a link in a rational homology sphere and some of its properties -- Ch. 3. Invariance of the surgery formula under a twist homeomorphism -- Ch. 4. The formula for surgeries starting from rational homology spheres -- Ch. 5. The invariant [lambda] for 3-manifolds with nonzero rank -- Ch. 6. Applications and variants of the surgery formula -- Appendix: More about the Alexander series. | |
| 588 | 0 | |a Print version record. | |
| 520 | |a 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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| contents | Ch. 1. Introduction and statements of the results -- Ch. 2. The Alexander series of a link in a rational homology sphere and some of its properties -- Ch. 3. Invariance of the surgery formula under a twist homeomorphism -- Ch. 4. The formula for surgeries starting from rational homology spheres -- Ch. 5. The invariant [lambda] for 3-manifolds with nonzero rank -- Ch. 6. Applications and variants of the surgery formula -- Appendix: More about the Alexander series. |
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| discipline | Mathematik |
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| id | ZDB-4-EBA-ocn887802708 |
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| indexdate | 2024-11-27T13:26:08Z |
| institution | BVB |
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| spelling | Lescop, Christine, 1966- https://id.oclc.org/worldcat/entity/E39PCjrG9PTvKpkqwqdJP69RXb http://id.loc.gov/authorities/names/n95101969 Global surgery formula for the Casson-Walker invariant / by Christine Lescop. Princeton : Princeton University Press, 1996. 1 online resource (150 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier text file Annals of mathematics studies ; number 140 Includes bibliographical references (pages 147-148) and index. Ch. 1. Introduction and statements of the results -- Ch. 2. The Alexander series of a link in a rational homology sphere and some of its properties -- Ch. 3. Invariance of the surgery formula under a twist homeomorphism -- Ch. 4. The formula for surgeries starting from rational homology spheres -- Ch. 5. The invariant [lambda] for 3-manifolds with nonzero rank -- Ch. 6. Applications and variants of the surgery formula -- Appendix: More about the Alexander series. Print version record. 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. In English. Surgery (Topology) http://id.loc.gov/authorities/subjects/sh85130792 Three-manifolds (Topology) http://id.loc.gov/authorities/subjects/sh85135028 Chirurgie (Topologie) Variétés topologiques à 3 dimensions. MATHEMATICS Topology. bisacsh Surgery (Topology) fast Three-manifolds (Topology) fast Manifolds. gtt Chirurgie (topologie) gtt Chirurgie (Topologie) ram Variétés topologiques à 3 dimensions. ram Print version: Lescop, Christine, 1966- Global surgery formula for the Casson-Walker invariant 0691021333 (DLC) 95045797 (OCoLC)33406805 Annals of mathematics studies ; no. 140. http://id.loc.gov/authorities/names/n42002129 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=818429 Volltext |
| spellingShingle | Lescop, Christine, 1966- Global surgery formula for the Casson-Walker invariant / Annals of mathematics studies ; Ch. 1. Introduction and statements of the results -- Ch. 2. The Alexander series of a link in a rational homology sphere and some of its properties -- Ch. 3. Invariance of the surgery formula under a twist homeomorphism -- Ch. 4. The formula for surgeries starting from rational homology spheres -- Ch. 5. The invariant [lambda] for 3-manifolds with nonzero rank -- Ch. 6. Applications and variants of the surgery formula -- Appendix: More about the Alexander series. Surgery (Topology) http://id.loc.gov/authorities/subjects/sh85130792 Three-manifolds (Topology) http://id.loc.gov/authorities/subjects/sh85135028 Chirurgie (Topologie) Variétés topologiques à 3 dimensions. MATHEMATICS Topology. bisacsh Surgery (Topology) fast Three-manifolds (Topology) fast Manifolds. gtt Chirurgie (topologie) gtt Chirurgie (Topologie) ram Variétés topologiques à 3 dimensions. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85130792 http://id.loc.gov/authorities/subjects/sh85135028 |
| title | Global surgery formula for the Casson-Walker invariant / |
| title_auth | Global surgery formula for the Casson-Walker invariant / |
| title_exact_search | Global surgery formula for the Casson-Walker invariant / |
| title_full | Global surgery formula for the Casson-Walker invariant / by Christine Lescop. |
| title_fullStr | Global surgery formula for the Casson-Walker invariant / by Christine Lescop. |
| title_full_unstemmed | Global surgery formula for the Casson-Walker invariant / by Christine Lescop. |
| title_short | Global surgery formula for the Casson-Walker invariant / |
| title_sort | global surgery formula for the casson walker invariant |
| topic | Surgery (Topology) http://id.loc.gov/authorities/subjects/sh85130792 Three-manifolds (Topology) http://id.loc.gov/authorities/subjects/sh85135028 Chirurgie (Topologie) Variétés topologiques à 3 dimensions. MATHEMATICS Topology. bisacsh Surgery (Topology) fast Three-manifolds (Topology) fast Manifolds. gtt Chirurgie (topologie) gtt Chirurgie (Topologie) ram Variétés topologiques à 3 dimensions. ram |
| topic_facet | Surgery (Topology) Three-manifolds (Topology) Chirurgie (Topologie) Variétés topologiques à 3 dimensions. MATHEMATICS Topology. Manifolds. Chirurgie (topologie) |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=818429 |
| work_keys_str_mv | AT lescopchristine globalsurgeryformulaforthecassonwalkerinvariant |