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This https://arxiv.org/abs/2503.05572 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Word problems and embedding-obstructions in cellular automata groups on groups
We study groups of reversible cellular automata, or CA groups, on groups. More generally, we consider automorphism groups of subshifts of finite type on groups. It is known that word problems of CA groups on virtually nilpotent groups are in co-NP, and can be co-NP-hard. We show that under the Gap Conjecture of Grigorchuk, their word problems are PSPACE-hard on all other groups. On free and surface groups, we show that they are indeed always in PSPACE. On a group with co-NEXPTIME word problem, …

This https://arxiv.org/abs/2505.13260 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Some remarks on Quillen's Dévissage theorem
In this paper we give a different proof of Quillen's Dévissage theorem using Barwick's theorem of the heart. The key ingredient is a certain short exact sequence of dg categories, which is closely related with the Auslander-type construction for nilpotent extensions which was used in the papers of Kuznetsov-Lunts \cite{KL15}, Land-Tamme \cite{LT19} and the author \cite{E20}.

This https://arxiv.org/abs/2304.07852 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Simplicity of crossed products by FC-hypercentral groups
In this paper, we give a complete, two-way characterization, of when a noncommutative crossed product $A \rtimes_λG$ is simple, in the case of $G$ being an FC-hypercentral group. This is a large class of amenable groups that contains all virtually nilpotent groups, and in the finitely-generated setting, coincides with the set of groups which have polynomial growth. We further completely characterize the ideal intersection property under the assumption that the group is FC, meaning that every e…