An extension of Casson's invariant by Kevin Walker

By Kevin Walker

This e-book describes an invariant, l, of orientated rational homology 3-spheres that is a generalization of labor of Andrew Casson within the integer homology sphere case. permit R(X) denote the gap of conjugacy periods of representations of p(X) into SU(2). allow (W, W, F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is said to be an properly outlined intersection variety of R(W) and R(W) inside of R(F). The definition of this intersection quantity is a fragile activity, because the areas concerned have singularities. A formulation describing how l transforms lower than Dehn surgical procedure is proved. The formulation includes Alexander polynomials and Dedekind sums, and will be used to provide a slightly undemanding facts of the life of l. it's also proven that after M is a Z-homology sphere, l(M) determines the Rochlin invariant of M

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