Lifting generic maps to embeddings. Triangulation and smoothing

Abstract

We show that if a non-degenerate PL map $f:N\to M$ lifts to a topological embedding in $M\times {\mathbb{R}}^k$ then it lifts to a PL embedding in there. We also show that if a stable smooth map $N^n\to M^m$, $m\ge n$, lifts to a topological embedding in $M\times \mathbb{R}$, then it lifts to a smooth embedding in there.

18 pages. In older versions, some content has moved between this paper and the companion paper arXiv:1711.03518