Towards a noncommutative Brouwer fixed-point theorem

TL;DR

This paper explores a noncommutative generalization of the Brouwer fixed-point theorem, proposing new results and conjectures inspired by the Borsuk-Ulam theorem, aiming to extend classical fixed-point concepts to noncommutative spaces.

Contribution

It introduces novel conjectures and partial results on extending the Brouwer fixed-point theorem to noncommutative settings, bridging classical topology and noncommutative geometry.

Findings

Proposes conjectures for noncommutative fixed-point theorems

Provides initial results supporting the conjectures

Suggests a new perspective inspired by Borsuk-Ulam theorem

Abstract

We present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk-Ulam theorem perspective.