Operad groups as a unified framework for Thompson-like groups

Werner Thumann

Published 2014-07-19, updated 2014-09-04Version 2

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.