Symmetry groups of four-manifolds

Details Symmetry groups of four-manifolds Symmetry groups of four-manifolds

1999-07-27

arxiv.org/abs/math/9907180v4

Topology 41 (4) 2002, pp. 835--851.

Mathematics

Geometric Topology

This is a substantially revised and shortened version. The argument has been streamlined by a more natural organization of the

Scientific paper

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.

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