Bültmann & Gerriets
Extension of Casson's Invariant. (AM-126), Volume 126
von Kevin Walker
Verlag: Princeton University Press
Reihe: Annals of Mathematics Studies
E-Book / PDF
Kopierschutz: Adobe DRM


Speicherplatz: 9 MB
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ISBN: 978-1-4008-8246-5
Erschienen am 02.03.2016
Sprache: Englisch
Umfang: 150 Seiten

Preis: 68,49 €

68,49 €
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Inhaltsverzeichnis
Klappentext


  • Frontmatter,
  • Contents,
  • 0. Introduction,
  • 1. Topology of Representation Spaces,
  • 2. Definition of ¿,
  • 3. Various Properties of ¿,
  • 4. The Dehn Surgery Formula,
  • 5. Combinatorial Definition of ¿,
  • 6. Consequences of the Dehn Surgery Formula,
  • A. Dedekind Sums,
  • B. Alexander Polynomials,
  • Bibliography,




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.