On Borel Anosov subgroups of SL(d, ℝ)

Dey, Subhadip¹

¹ Department of Mathematics, Yale University, New Haven, CT, United States

Geometry & topology, Tome 29 (2025) no. 1, pp. 171-192.

Résumé

We study the antipodal subsets of the full flag manifolds $\mathcal{ℱ}({ℝ}^d)$. As a consequence, for natural numbers $d\ge 2$ such that $d\ne 5$ and $d\not\equiv 0,\pm 1mod8$, we show that Borel Anosov subgroups of $\mathrm{SL}(d,ℝ)$ are virtually isomorphic to either a free group or the fundamental group of a closed hyperbolic surface. This gives a partial answer to a question asked by Andrés Sambarino. Furthermore, we show restrictions on the hyperbolic spaces admitting uniformly regular quasi-isometric embeddings into the symmetric space $X_d$ of $\mathrm{SL}(d,ℝ)$.

Détail

DOI : 10.2140/gt.2025.29.171

Keywords: Anosov representations, flag manifolds

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