Symmetry groups of four-manifolds

If a (possibly finite) compact Lie group acts effectively, locally linearly, and homologically trivially on a closed, simply connected four-manifold M with b(2)(M) greater than or equal to 3, 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. (C) 2002 Elsevier Science Ltd. All rights reserved.