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An intersection theory count of the -representations of the fundamental group of a 3-manifold

Curtis, Cynthia (Elsevier, 2001)

We define an invariant of closed 3-manifolds counting the signed equivalence classes of representations of the fundamental group in . The invariant is an -analog of the Casson-Walker invariant for SU(2). We reinterpret the ...

A Dehn surgery description of regular finite cyclic covering spaces of rational homology spheres

Curtis, Cynthia (World Scientific Publishing, 2001)

We provide related Dehn surgery descriptions for rational homology spheres and a class of their regular finite cyclic covering spaces. As an application, we use the surgery descriptions to relate the Casson invariants of ...

A PSL(2,C) Casson Invariant

Curtis, Cynthia (American Mathematical Society, 2005)

We use intersection theory techniques to define an invariant of closed 3-manifolds counting the characters of irreducible representations of the fundamental group in PSL(2,C). We note several properties of the invariant ...

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.

Erratum to “An intersection theory count of the SL(2,C)-representations of the fundamental group of a 3-manifold.”

Curtis, Cynthia (Elsevier, 2003)

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 ...