A probabilistic approach to exhaustion in the infinite-genus case

TL;DR

This paper investigates a probabilistic method for exhaustion in infinite-genus complexes using random simplicial complexes, aiming to support rigidity properties relevant to geometric group theory.

Contribution

It introduces a probabilistic framework for exhaustion in infinite-genus complexes, extending Costa and Farber's model to analyze rigidity phenomena.

Findings

Probabilistic evidence for exhaustion via rigid expansions.

Application of random simplicial complexes to infinite-genus cases.

Potential implications for action rigidity and Ivanov's meta-conjecture.

Abstract

We explore the use of Costa and Farber's model for random simplicial complexes to give probabilistic evidence for exhaustion via rigid expansions on random simplicial complexes which are analogous of curve complexes. This has potential applications to action rigidity following Ivanov's meta-conjecture.