One-dimensional polyhedral irregular sets of homomorphisms of 3-manifolds

Abstract

Examples are given to show that there exist homeomorphisms of open 3 3 -manifolds whose sets of irregular points are wildly embedded one-dimensional polyhedra. The main result of the paper is that a one-dimensional polyhedral set of irregular points can fail to be locally tame on, at most, a discrete subset of the set of points of order greater than one. Necessary and sufficient conditions are given so that the set of irregular points is locally tame at each point.