On Borel Anosov subgroups of SL(d, ℝ)

Dey, Subhadip

doi:10.2140/gt.2025.29.171

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On Borel Anosov subgroups of ${\rm SL}(d,\mathbb{R})$

Subhadip Dey

Geometry & Topology 29 (2025) 171–192

DOI: 10.2140/gt.2025.29.171

Abstract

We study the antipodal subsets of the full flag manifolds $ℱ (ℝ^{d})$ . As a consequence, for natural numbers $d \geq 2$ such that $d \neq 5$ or $d ≢ 0, \pm 1 mod 8$ , we show that Borel Anosov subgroups of $SL (d, ℝ)$ 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 $SL (d, ℝ)$ .

Dedicated to Misha Kapovich on the occasion of his 60th birthday

Keywords

Anosov representations, flag manifolds

Mathematical Subject Classification

Primary: 14M15, 20F65, 22E40

References

Publication

Received: 9 October 2022

Revised: 25 December 2023

Accepted: 18 May 2024

Published: 1 January 2025

Proposed: David Fisher

Seconded: Mladen Bestvina, Anna Wienhard

Authors

Subhadip Dey
Department of Mathematics Yale University New Haven, CT United States

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Volume 29, issue 1 (2025)