An equivariant Casson invariant of knots in homology spheres
نویسنده
چکیده
From the construction of the Casson invariant of homology spheres using intersection on configuration spaces, we propose a construction of an equivariant Casson invariant for a knot K homologous to 0 in rational homology sphere M . Our construction is adapted from C. Lescop ([7]) and use the same ideas in an equivariant setting. We show that the invariant we obtain is similar to the 2-loop part of the rational Kontsevich integral, and may be equal. We check that it codes the Casson invariants of the cyclic ramified coverings of M along K in exactly the same way as found by S. Garoufalidis and A. Kricker for the 2-loop invariant ([2]).
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