Symmetry groups of four-manifolds
| dc.creator | McCooey, Michael P. | |
| dc.date | 1999-07-27 | |
| dc.date | 2000-05-30 | |
| dc.date.accessioned | 2026-07-07T08:20:20Z | |
| dc.date.available | 2026-07-07T08:20:20Z | |
| dc.description | If a (possibly finite) compact Lie group acts effectively, locally linearly, and homologically trivially on a closed, simply-connected four-manifold with second Betti number at least three, then it must be isomorphic to a subgroup of S^1 x S^1, and the action must have nonempty fixed-point set. Our results strengthen and complement recent work by Edmonds, Hambleton and Lee, and Wilczynski, among others. Our tools include representation theory, finite group theory, and Borel equivariant cohomology. | |
| dc.description | This is a substantially revised and shortened version. The argument has been streamlined by a more natural organization of the "minimal bad" cases and a much simplified treatment of rank 2 nonabelian groups (such as the eight-element dihedral group) using results from "Four-manifolds which admit Z_p x Z_p actions" (math.GT/0002187). The main result has also been sharpened slightly by appeal to the G-signature theorem, and now covers manifolds with the cohomology of CP^2 # CP^2. 15 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/9907180 | |
| dc.identifier | http://arxiv.org/abs/math/9907180 | |
| dc.identifier | Topology 41 (4) 2002, pp. 835--851. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135044 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.subject | Group Theory | |
| dc.subject | 57S17, 57S25 | |
| dc.title | Symmetry groups of four-manifolds | |
| dc.type | text |