Aspects of group actions on four-manifolds

AbstractA collection of various consequences of the existence of finite cyclic group actions on simply connected topological 4-manifolds, with an emphasis on involutions, is presented as a complement to various known constructions of group actions on these manifolds. The relationship between the representation on integral cohomology and the fixed-point set is described. The significance of a spin structure on the 4-manifold for the fixed-point set of a locally linear involution is described, leading to examples of 4-manifolds admitting no locally linear involution. Further restrictions on the two-dimensional parts of the fixed-point set of an involution are derived