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arXiv · 2207.09151

Mixed identities, hereditarily separated actions and oscillation

Aleksander Ivanov·Roland Zarzycki
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Abstract

Given a topological $G$-space we consider equations with parameters over $G$. In particular we formulate some very general conditions on words with parameters $w(\bar{y},\bar{g})$ over $G$ which guarantee that the inequality $w(\bar{y},\bar{g})\neq 1$ has a solution in $G$. These results are illustrated in some typical situations, in particular standard actions of Thompson's group $F$ and branch groups are considered. The major results of this paper appeared in some form in Section 2 of the PhD thesis of the second author (avalable at arXiv:1308.6330).

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Aleksander Ivanov, Roland Zarzycki. 2022-07-19. Mixed identities, hereditarily separated actions and oscillation. https://doi.org/10.1515/jgth-2023-0028

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