Nearly geodesic immersions and domains of discontinuity

Davalo, Colin

doi:10.2140/gt.2025.29.2391

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Nearly geodesic immersions and domains of discontinuity

Colin Davalo

Geometry & Topology 29 (2025) 2391–2461

DOI: 10.2140/gt.2025.29.2391

Abstract

We study nearly geodesic immersions in higher-rank symmetric spaces of noncompact type, which we define as immersions that satisfy a bound on their fundamental form, generalizing the notion of immersions in hyperbolic space with principal curvature in $(- 1, 1)$ . This notion depends on the choice of a flag manifold embedded in the visual boundary, and immersions satisfying this bound admit a natural domain in this flag manifold that comes with a fibration. As an application we give an explicit fibration of some domains of discontinuity for some Anosov representations. Our method can be applied in particular to some $Θ$ -positive representations for each notion of $Θ$ -positivity.

Keywords

domains of discontinuity, Anosov representations, symmetric spaces of noncompact type

Mathematical Subject Classification

Primary: 53C35

Secondary: 22E40

References

Publication

Received: 31 March 2023

Revised: 7 May 2024

Accepted: 30 August 2024

Published: 14 August 2025

Proposed: Anna Wienhard

Seconded: David Fisher, Ian Agol

Authors

Colin Davalo
Mathematisches Institut Ruprecht-Karls Universität Heidelberg Heidelberg Germany

Open Access made possible by participating institutions via Subscribe to Open.

Volume 29, issue 5 (2025)