An Extension of Casson's Invariant to Rational Homology Spheres
نویسندگان
چکیده
In 1985, Andrew Casson defined an invariant À(M) of an oriented integral homology 3-sphere M [C, AM]. This invariant can be thought of as counting the number of conjugacy classes of nontrivial representations nx (M) —• SU(2), in the sense that the Lefschetz number of a map counts the number of fixed points. Casson proved the following three properties of A. (i) If nx(M) = 1, then A(M) = 0. (ii) Let N be the complement of a knot in a homology sphere and let N{, denote TV Dehn surgered along one meridian and n longitudes (see below for terminology). Then
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