Rohlin's invariant and gauge theory, I. Homology 3-tori

dc.creatorRuberman, Daniel
dc.creatorSaveliev, Nikolai
dc.date2003-02-11
dc.date2003-06-09
dc.date.accessioned2026-07-07T04:55:13Z
dc.date.available2026-07-07T04:55:13Z
dc.descriptionThis is the first in a series of papers exploring the relationship between the Rohlin invariant and gauge theory. We discuss the Casson-type invariant of a 3-manifold with the integral homology of a torus, given by counting projectively flat connections. We show that its mod 2 evaluation is given by the triple cup product in cohomology, and so it coincides with a sum of Rohlin invariants. Our counting argument makes use of a natural action of the first cohomology on the moduli space of projectively flat connections; along the way we construct perturbations that are equivariant with respect to this action. Combined with the Floer exact triangle, this gives a purely gauge-theoretic proof that Casson's homology sphere invariant reduces mod 2 to the Rohlin invariant.
dc.descriptionChanged title to fit with succeeding papers in series. Added reference to Turaev's work
dc.identifierhttps://arxiv.org/abs/math/0302131
dc.identifierhttp://arxiv.org/abs/math/0302131
dc.identifierComm. Math. Helv., 79 (2004), no. 3, 618--646.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66502
dc.subjectGeometric Topology
dc.subject57N10
dc.titleRohlin's invariant and gauge theory, I. Homology 3-tori
dc.typetext

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