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An extension of Casson’s invariant to rational homology spheres. (English) Zbl 0699.57008

Casson defined his invariant for oriented homology-3-spheres (integer coefficients). In the present note, describing results of the author’s thesis, a generalization of Casson’s construction is given extending the invariant to the case of rational homology-3-spheres (rational coefficients), again starting from representations of their fundamental groups in SU(2). A Dehn-surgery formula is given for the generalized invariant, which can be used to define it directly. For a further extension, see the next review (Zbl 0699.57009). Another generalization of Casson’s invariant to rational homology-3-spheres is given in a paper of Boyer and Nicas; see also a paper by S. Boyer and D. Lines [J. Reine Angew. Math. 405, 181-220 (1990; Zbl 0691.57004)], in which the case of homology lens spaces is considered.
Reviewer: B.Zimmermann

MSC:

57N10 Topology of general \(3\)-manifolds (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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References:

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