Download An extension of Casson's invariant by Kevin Walker PDF

By Kevin Walker

This publication 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. allow R(X) denote the gap of conjugacy periods of representations of p(X) into SU(2). enable (W, W, F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is said to be an correctly outlined intersection variety of R(W) and R(W) within 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 comprises Alexander polynomials and Dedekind sums, and will be used to offer a slightly easy facts of the lifestyles of l. it's also proven that once M is a Z-homology sphere, l(M) determines the Rochlin invariant of M

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