An extension of Casson’s invariant. (English) Zbl 0752.57011

Annals of Mathematics Studies. 126. Princeton, NJ: Princeton University Press,. v, 131 p. (1992).
A. Casson introduced in 1985 an integer-valued invariant \(\lambda\) of oriented \(\mathbb{Z}\)-homology 3-spheres. [For a good exposition see S. Akbulut and J. McCarthy, Casson’s invariant for oriented homology 3-spheres — an exposition (1990; Zbl 0695.57011)]. The present author has subsequently generalized Casson’s invariant to \(\mathbb{Q}\)-homology 3- spheres [Bull. Am. Math. Soc., New. Ser. 22, 261-267 (1990; Zbl 0699.57008)]. This monograph presents the details of his work [loc. cit.]. It consists of six chapters (Topology of representation spaces, Definition of \(\lambda\), Various properties of \(\lambda\), The Dehn surgery formula, Combinatorial definition of \(\lambda\), and Consequences of the Dehn surgery formula) and two appendices (Dedekind sums and Alexander polynomials).


57N10 Topology of general \(3\)-manifolds (MSC2010)
57M35 Dehn’s lemma, sphere theorem, loop theorem, asphericity (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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