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arXiv · 2607.28001

Centralizers and classifying spaces for commutativity of $SL_2(\mathbb{Z}[1/p])$

Omar Antol\'ın-Camarena·Ramón Flores·Luis Jorge Sánchez Saldaña
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Abstract

We compute the homotopy type of the classifying space for commutativity introduced by Adem, F. Cohen and Torres-Giese for the group $\SL_2(\Z[1/p])$, both as a discrete topological group and with the subspace topology from $\SL_2(\R)$. Doing so requires compiling detailed information on the maximal abelian subgroups of $\SL_2(\Z[1/p])$, which turn out to be precisely the centralizers of the non-central elements of the group, for which we employ methods from geometric group theory.

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Omar Antol\'ın-Camarena, Ramón Flores, Luis Jorge Sánchez Saldaña. 2026-07-30. Centralizers and classifying spaces for commutativity of $SL_2(\mathbb{Z}[1/p])$. https://arxiv.org/abs/2607.28001

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