About the Bloch-Connelly-Henderson Theorem on the simplexwise linear homeomorphisms of a convex 2-disk

TL;DR

This paper improves the proof of the Bloch-Connelly-Henderson theorem concerning the structure of space of simplexwise linear homeomorphisms of a convex 2-disk, enhancing understanding of their topological properties.

Contribution

It provides an improved proof of the theorem, especially refining the main lemma, advancing the theoretical understanding of $SL$ homeomorphisms on convex 2-disks.

Findings

Enhanced proof of the theorem with a better main lemma

Deeper insight into the topology of $SL$ homeomorphisms

Potential applications to convex geometry and topological studies

Abstract

This paper gives an improved version of the original proof of Bloch-Connelly-Henderson's theorem about the space of $SL$ homeomorphisms of a convex 2-disk. A major improvement is related to the main lemma of the original paper.