Locally compact groups with varying finiteness length

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• Yuri Santos Rego (Lincoln)
• Friday 18 October 2024, 13:45-14:45
• MR13.

If you have a question about this talk, please contact Francesco Fournier-Facio.

We shall discuss in this talk finiteness (or compactness) properties for locally compact groups that extend the notions of ‘finite’ (compact) generation and of ‘finite’ (compact) presentation. We will see what is currently known about groups with specified compactness properties, and shifting focus to the totally disconnected case I shall present a construction of (nondiscrete) tdlc groups with prescribed compactness properties. Along the way we obtain some other results: a new family of (discrete) Thompson-like groups containing, for every n, groups of homological type FP_n but not of type FP_{n+1}; and a family of tdlc groups acting nicely on some CAT cube complexes. This is ongoing joint work with Ilaria Castellano, Bianca Marchionna, and Brita Nucinkis.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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