Symmetry Groups of Four-manifolds
نویسنده
چکیده
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 3, then it must be isomorphic to a subgroup of S × S, and the action must have nonempty fixed-point set. Our results strengthen and complement recent work by Edmonds, Hambleton and Lee, and Wilczyński, among others. Our tools include representation theory, finite group theory, and Borel equivariant cohomology for nonabelian groups. In some cases, we calculate this cohomology directly, while in others, we first localize with respect to different multiplicative subsets of cohomology rings. We briefly review the essential background.
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