Automorphism groups of cocompact CAT(0) cube complexes and simplicity
Autor: | Hartnick, Tobias, Incerti-Medici, Merlin |
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Rok vydání: | 2023 |
Předmět: | |
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 |
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