Automorphism groups of cocompact CAT(0) cube complexes and simplicity

Autor:	Hartnick, Tobias, Incerti-Medici, Merlin
Rok vydání:	2023
Předmět:	Mathematics - Group Theory 22D05 20E32 20E08 20F65
Druh dokumentu:	Working Paper
Popis:	We provide a systematic description of the automorphism groups of specially cocompact CAT(0) cube complexes. We show that these groups are topologically finitely generated, present a method to explicitly obtain generating sets, and prove a dichotomy on their size. Furthermore, we show that, under some extra assumptions, the normal subgroup known as Aut^+ is simple, non-discrete, and tdlc. In particular, we obtain a new class of simple, non-discrete, tdlc groups that are accessible to further study. Finally, we study the relative size of Aut^+ in the automorphism group, providing a sufficient condition for its closure to be finite index and presenting a common example where it is not even cocompact. Comment: 77 pages, 7 figures, comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.03336 Zobrazit plný text záznamu View this record from Arxiv