Geometric invariants of TDLC completions

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• Ilaria Castellano (Heinrich-Heine-Universität Düsseldorf)
• Monday 28 July 2025, 14:00-15:00
• Seminar Room 1, Newton Institute.

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OGGW01 - Discrete and profinite groups

Let $\Gamma$ be a Hausdorff topological group and $\Lambda$ an open commensurated subgroup of $\Gamma$. A TDLC completion (short for totally disconnected locally compact completion) of $(\Gamma,\Lambda)$ is a pair $(G,\phi)$ where: $G$ is a TDLC group, $\phi\colon \Gamma\to G$ is a continuous homomorphism with dense image and $\Lambda=\phi^{-1}(L)$ for some compact open subgroup $L\subseteq G$. One important example is given by Schlichting completions.   Recently, Bonn and Sauer showed that, from the point of view of compactness properties, the Schlichting completion of a pair $(\Gamma,\Lambda)$ acts precisely as if it were the quotient of $\Gamma$ by $\Lambda$ [BS24]. Motivated by this result, José Pedro Quintanilha and I set out to explore whether a similar phenomenon holds for the $\Sigma$-sets [BHQ24a,BHQ24b].   In this talk, I will present the results of our project [CQ25], along with some of its applications.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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