Rohlin's invariant and gauge theory, I. Homology 3-tori
| dc.creator | Ruberman, Daniel | |
| dc.creator | Saveliev, Nikolai | |
| dc.date | 2003-02-11 | |
| dc.date | 2003-06-09 | |
| dc.date.accessioned | 2026-07-07T04:55:13Z | |
| dc.date.available | 2026-07-07T04:55:13Z | |
| dc.description | This 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.description | Changed title to fit with succeeding papers in series. Added reference to Turaev's work | |
| dc.identifier | https://arxiv.org/abs/math/0302131 | |
| dc.identifier | http://arxiv.org/abs/math/0302131 | |
| dc.identifier | Comm. Math. Helv., 79 (2004), no. 3, 618--646. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66502 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N10 | |
| dc.title | Rohlin's invariant and gauge theory, I. Homology 3-tori | |
| dc.type | text |