Geodesic
Klein-four connections and the Casson invariant for nontrivial admissible U(2) bundles
Scaduto, Christopher1 ; Stoffregen, Matthew2
1 Department of Mathematics, Brandeis University, Waltham, MA, United States
2 Department of Mathematics, University of California, Los Angeles, CA, United States
Algebraic and Geometric Topology, Tome 17 (2017) no. 5, pp. 2841-2861

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Given a rank-2 hermitian bundle over a 3–manifold that is nontrivial 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.

DOI : 10.2140/agt.2017.17.2841
Classification : 57M27
Keywords: Casson invariant, Lescop invariant, $2$–torsion

Scaduto, Christopher 1 ; Stoffregen, Matthew 2

1 Department of Mathematics, Brandeis University, Waltham, MA, United States
2 Department of Mathematics, University of California, Los Angeles, CA, United States 
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Scaduto, Christopher; Stoffregen, Matthew. Klein-four connections and the Casson invariant for nontrivial admissible U(2) bundles. Algebraic and Geometric Topology, Tome 17 (2017) no. 5, pp. 2841-2861. doi: 10.2140/agt.2017.17.2841

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