Klein-four connections and the Casson invariant for non-trivial admissible $U(2)$ bundles
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2016
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| _version_ | 1866909306927972352 |
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| author | Scaduto, Christopher Stoffregen, Matthew |
| author_facet | Scaduto, Christopher Stoffregen, Matthew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1605_01016 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Klein-four connections and the Casson invariant for non-trivial admissible $U(2)$ bundles Scaduto, Christopher Stoffregen, Matthew Geometric Topology 57M27 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. |
| title | Klein-four connections and the Casson invariant for non-trivial admissible $U(2)$ bundles |
| topic | Geometric Topology 57M27 |
| url | https://arxiv.org/abs/1605.01016 |