Presentation complexes with the fixed point property

TL;DR

This paper constructs a specific compact 2D polyhedron with the fixed point property and even Euler characteristic, answering longstanding questions posed by Bing since 1969.

Contribution

It provides the first example of such a polyhedron, resolving two open questions by Bing from 1969.

Findings

Existence of a compact 2D polyhedron with fixed point property and even Euler characteristic

Answers to Bing's questions from 1969

Advancement in understanding fixed point properties in topology

Abstract

We prove that there exists a compact two-dimensional polyhedron with the fixed point property and even Euler characteristic. This answers a question posed by R.H. Bing in 1969. We also settle another of Bing's questions.