The existence of thick triangulations -- an "elementary" proof

TL;DR

This paper presents a simpler, elementary proof for the existence of thick triangulations in noncompact  manifolds, highlighting the role of curvature and using basic differential topology tools.

Contribution

It offers a more accessible proof of thick triangulation existence, reducing reliance on complex methods and emphasizing curvature's importance.

Findings

Thick triangulations exist for noncompact  manifolds.

The proof simplifies previous approaches using elementary differential topology.

Curvature plays a significant role in the triangulation construction.

Abstract

We provide an alternative, simpler proof of the existence of thick triangulations for noncompact $\mathcal{C}^1$ manifolds. Moreover, this proof is simpler than the original one given in \cite{pe}, since it mainly uses tools of elementary differential topology. The role played by curvatures in this construction is also emphasized.