Klein-four connections and the Casson invariant for non-trivial admissible $U(2)$ bundles

Christopher Scaduto; Matthew Stoffregen

doi:10.2140/agt.2017.17.2841

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arXiv · 1605.01016

Klein-four connections and the Casson invariant for non-trivial admissible $U(2)$ bundles

Christopher Scaduto·Matthew Stoffregen

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Abstract

Given a rank 2 hermitian bundle over a 3-manifold that is non-trivial admissible in the sense of Floer, one defines its Casson invariant as half the signed count of its projectively flat connections, suitably perturbed. We show that the 2-divisibility of this integer invariant is controlled in part by a formula involving the mod 2 cohomology ring of the 3-manifold. This formula counts flat connections on the induced adjoint bundle with Klein-four holonomy.

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Christopher Scaduto, Matthew Stoffregen. 2016-05-03. Klein-four connections and the Casson invariant for non-trivial admissible $U(2)$ bundles. https://doi.org/10.2140/agt.2017.17.2841

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