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Record Nr. |
UNINA9910154744603321 |
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Autore |
Walker Kevin |
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Titolo |
An Extension of Casson's Invariant. (AM-126), Volume 126 / / Kevin Walker |
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Pubbl/distr/stampa |
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Princeton, NJ : , : Princeton University Press, , [2016] |
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©1992 |
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ISBN |
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Descrizione fisica |
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1 online resource (140 pages) : illustrations |
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Collana |
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Annals of Mathematics Studies ; ; 308 |
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Classificazione |
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Disciplina |
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Soggetti |
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Three-manifolds (Topology) |
Invariants |
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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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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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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 |
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Sommario/riassunto |
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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. |
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