Pseudofree Finite Group Actions on 4-Manifolds

Abstract

We prove several theorems about the pseudofree, locally linear and homologically trivial action of finite groups 𝐺 on closed, connected, oriented 4-manifolds 𝑀 with non-zero Euler characteristic. In this setting, the rank𝑝 (𝐺) ≤ 1, for 𝑝 ≥ 5 prime and rank(𝐺) ≤ 2, for 𝑝 = 2, 3. We combine these results into two main theorems: Theorem A and Theorem B in Chapter 1. These results strengthen the work done by Edmonds, and Hambleton and Pamuk. We remark that for low second betti-numbers ( <= 2) there are other examples of finite groups which can act in the above way.