Klein-four connections and the Casson invariant for nontrivial admissible U(2) bundles
| Autor: | Matthew Stoffregen, Christopher Scaduto |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
$2$–torsion 010102 general mathematics Lescop invariant Geometric Topology (math.GT) Casson invariant 16. Peace & justice Mathematics::Geometric Topology 01 natural sciences Mathematics - Geometric Topology 57M27 0103 physical sciences FOS: Mathematics Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Algebr. Geom. Topol. 17, no. 5 (2017), 2841-2861 |
| ISSN: | 1472-2739 1472-2747 |
| DOI: | 10.2140/agt.2017.17.2841 |
| Popis: | 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. Comment: 17 pages, 2 figures |
| Databáze: | OpenAIRE |
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