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The SL(2,C) Casson invariant for Seifert fibered homology spheres and surgeries on twist knots

Curtis, Cynthia; Boden, Hans U. (World Scientific Publishing, 2006)

We derive a simple closed formula for the SL(2,C) Casson invariant for Seifert fibered homology 3-spheres using the correspondence between SL(2,C) character varieties and moduli spaces of parabolic Higgs bundles of rank ...

Splicing and the SL(2,C) invariant

Curtis, Cynthia; Boden, Hans U. (American Mathematical Society, 2008)

We establish a formula for the SL2(C) Casson invariant of spliced sums of homology spheres along knots. Along the way, we show that the SL2(C) Casson invariant vanishes for spliced sums along knots in S-3.