Branched coverings and equivariant smoothings of 4-manifolds

Abstract

This paper describes some new families of finite group actions on 4-manifolds, including infinite families of smoothly inequivalent actions which are topologically equivalent and locally linear actions which are not smoothable. The constructions involve a variety of results on 4-manifolds and branched coverings. One common feature is that these families are counterexamples to the Lashof–Rothenberg homotopy classication results for equivariant smoothings which hold for actions with no 4-dimensional strata. Related examples with 4-dimensional fixed point sets are also described.