TL;DR
This paper introduces the Neretin group of spheromorphisms of an infinite regular tree, discusses its natural topology, and presents a proof of its simplicity, contributing to the understanding of totally disconnected locally compact groups.
Contribution
It defines the Neretin group, describes its natural topology, and provides a proof of its simplicity, clarifying its structure within totally disconnected groups.
Findings
The Neretin group is a simple, totally disconnected locally compact group.
The natural topology of the Neretin group differs from the usual guess.
The paper confirms the simplicity of the Neretin group.
Abstract
This is the extended version of the talk we gave during the Arbeitsgemeinschaft on totally disconnected locally compact groups, held in Oberwolfach in October 2014. We give the definition of the Neretin group of spheromorphisms of the infinite -regular tree, and describe its natural totally disconnected group topology, which is not the one that usually appears as the first guess. We also present the proof of simplicity due to Kapoudjian. We do not make any claims concerning the originality of the presented results.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.