THE SL2(ℂ) CASSON INVARIANT FOR SEIFERT FIBERED HOMOLOGY SPHERES AND SURGERIES ON TWIST KNOTS Academic Article uri icon

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abstract

  • We derive a simple closed formula for the SL2(ℂ) Casson invariant for Seifert fibered homology 3-spheres using the correspondence between SL2(ℂ) character varieties and moduli spaces of parabolic Higgs bundles of rank two. These results are then used to deduce the invariant for Dehn surgeries on twist knots by combining computations of the Culler-Shalen norms with the surgery formula for the SL2(ℂ) Casson invariant.

publication date

  • September 2006