An Extension of Casson's Invariant. (AM-126), Volume 126 / / Kevin Walker
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| Autore: |
Walker Kevin
|
| Titolo: |
An Extension of Casson's Invariant. (AM-126), Volume 126 / / Kevin Walker
|
| Pubblicazione: | Princeton, NJ : , : Princeton University Press, , [2016] |
| ©1992 | |
| Descrizione fisica: | 1 online resource (140 pages) : illustrations |
| Disciplina: | 514/.3 |
| Soggetto topico: | Three-manifolds (Topology) |
| Invariants | |
| Soggetto non controllato: | Absolute value |
| Andrew Casson | |
| Basis (linear algebra) | |
| Cohomology | |
| Dan Freed | |
| Dehn surgery | |
| Dehn twist | |
| Determinant | |
| Diagram (category theory) | |
| Disk (mathematics) | |
| Elementary proof | |
| Fundamental group | |
| General position | |
| Heegaard splitting | |
| Homology sphere | |
| Identity matrix | |
| Inner product space | |
| Lie group | |
| Mathematical sciences | |
| Morris Hirsch | |
| Normal bundle | |
| Scientific notation | |
| Sequence | |
| Surjective function | |
| Symplectic geometry | |
| Theorem | |
| Topology | |
| Classificazione: | SK 320 |
| Nota di bibliografia: | Includes bibliographical references. |
| Nota di contenuto: | Frontmatter -- Contents -- 0. Introduction -- 1. Topology of Representation Spaces -- 2. Definition of λ -- 3. Various Properties of λ -- 4. The Dehn Surgery Formula -- 5. Combinatorial Definition of λ -- 6. Consequences of the Dehn Surgery Formula -- A. Dedekind Sums -- B. Alexander Polynomials -- Bibliography |
| Sommario/riassunto: | This book describes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case. Let R(X) denote the space of conjugacy classes of representations of p(X) into SU(2). Let (W,W,F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is declared to be an appropriately defined intersection number of R(W) and R(W) inside R(F). The definition of this intersection number is a delicate task, as the spaces involved have singularities. A formula describing how l transforms under Dehn surgery is proved. The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of l. It is also shown that when M is a Z-homology sphere, l(M) determines the Rochlin invariant of M. |
| Titolo autorizzato: | An Extension of Casson's Invariant. (AM-126), Volume 126 |
| ISBN: | 1-4008-8246-X |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910154744603321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Annals of mathematics studies ; ; no. 126.