Operad groups as a unified framework for Thompson-like groups

TL;DR

This paper introduces a unified operad-based framework for Thompson-like groups, providing new conditions for these groups to have certain finiteness properties and extending previous results conceptually.

Contribution

It develops a novel operad and category theory framework that unifies and generalizes existing Thompson-like groups and their properties.

Findings

Operad groups can be used to analyze Thompson-like groups.

Provided sufficient conditions for operad groups to be of type F_infinity.

Unified and extended previous proofs for finiteness properties of these groups.

Abstract

We propose a new unified framework for Thompson-like groups using a well-known device called operads and category theory as language. We discuss examples of operad groups which have appeared in the literature before. As a first application, we give sufficient conditions for plain operads to yield groups of type $F_\infty$. This unifies and extends existing proofs for certain Thompson-like groups in a conceptual manner.