Piecewise linear groups and transformation groups

Abstract

The object of this paper is to show, via specific theorems, that the notions of topological group and transformation group become severely restricted when transposed to the piecewise linear category. Let us understand a piecewise linear (PL) group to be a topological group G together with a piecewise linear structure on G (i.e., triangulation of G as a locally finite simplicial complex), in terms of which the group multiplication G x G -> G and inversion G -> G are given by piecewise linear functions.