Open Access
Translator Disclaimer
2017 Klein-four connections and the Casson invariant for nontrivial admissible $U(2)$ bundles
Christopher Scaduto, Matthew Stoffregen
Algebr. Geom. Topol. 17(5): 2841-2861 (2017). DOI: 10.2140/agt.2017.17.2841

Abstract

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.

Citation

Download Citation

Christopher Scaduto. Matthew Stoffregen. "Klein-four connections and the Casson invariant for nontrivial admissible $U(2)$ bundles." Algebr. Geom. Topol. 17 (5) 2841 - 2861, 2017. https://doi.org/10.2140/agt.2017.17.2841

Information

Received: 28 August 2016; Revised: 2 June 2017; Accepted: 20 June 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06791386
MathSciNet: MR3704245
Digital Object Identifier: 10.2140/agt.2017.17.2841

Subjects:
Primary: 57M27

Rights: Copyright © 2017 Mathematical Sciences Publishers

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.17 • No. 5 • 2017
MSP
Back to Top