Fixed point theorem for reflexive Banach spaces and uniformly convex non positively curved metric spaces

TL;DR

This paper extends fixed point theorems to reflexive Banach spaces and uniformly convex Busemann spaces, providing new criteria for group actions on simplicial complexes, broadening the scope of geometric fixed point results.

Contribution

It generalizes existing fixed point theorems to more general spaces, including reflexive Banach and uniformly convex Busemann spaces, for group actions on simplicial complexes.

Findings

Established a new fixed point criterion for groups acting on simplicial complexes.

Extended fixed point theorems to reflexive Banach spaces.

Generalized results previously known for specific spaces.

Abstract

This article generalizes the work of Ballmann and \'Swiatkowski to the case of Reflexive Banach spaces and uniformly convex Busemann spaces, thus giving a new fixed point criterion for groups acting on simplicial complexes.