Piecewise Linear Critical Levels and Collapsing

Abstract

In this paper the idea of collapsing, and the associated idea of handle cancellation, in a piecewise linear manifold are used to produce a version of Morse theory for piecewise linear embeddings. As an application of this it is shown that, if $n > 2$, there exist triangulations of the $n$-ball that are not simplicially collapsible.