Locally linear actions on 3-manifolds

Abstract

Let a finite groupGact topologically on a closed smooth manifoldMn. One of the most natural and basic questions is whether such an action can be smoothed. More precisely, let γ:G×Mn→Mnbe a topological action ofGonMn. The action γ can be smoothed if there exists a smooth actionand an equivariant homeomorphismIt is well known that forn≤ 2 every finite topological group action onMnis smoothable. However already forn= 3 there are examples of topological actions on 3-manifolds which cannot be smoothed (see [1, 2] and references there). All these actions fail to be smoothable because of bad local behaviour.