Collin Bleak - Embeddings into Finitely Presented Simple Groups

This talk was part of the Workshop on "Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics" held at the ESI July 17 — 21, 2023.

In this talk, we describe a process whereby we can embed any hyperbolic group into a finitely presented infinite simple group. This gives a proof of what is, in some sense, the ​``typical'' case of the Boone-Higman Conjecture of 1973 (that a finitely generated grouip G has a solvable word problem if and only if G can be embedded into a finitely generated simple group).

The talk will proceed in three roughly independent parts: A short history of the Boone-Higman conjecture, a discussion of hyperbolic groups and an embedding of these into the Rational group of Grigorchuk, Nekrashevych, and Suschanskii, and finally, a discussion of why the topological full group over this rational group is finitely presented and simple, or, at least provides a route to a further embedding into a group that is finitely presented and simple.

Joint with James Belk, Francesco Matucci, and Matthew Zaremsky.

Видео Collin Bleak - Embeddings into Finitely Presented Simple Groups канала Erwin Schrödinger International Institute for Mathematics and Physics (ESI)