We consider the action of Anosov subgroups of a semi-simple Lie group on the associated flag manifolds. A systematic approach to construct cocompact domains of discontinuity for this action was given by Kapovich, Leeb and Porti in arXiv:1306.3837. For ∆-Anosov representations, we prove that every cocompact domain of discontinuity arises from this construction, up to a few exceptions in low rank. Then we compute which flag manifolds admit these domains and, in some cases, the number of domains. We also find a new compactification for locally symmetric spaces arising from maximal representations into \mathrmSp(4n+2,\mathbb R).
SEEK ID: https://publications.h-its.org/publications/980
Research Groups: Groups and Geometry
Publication type: Journal
Journal: arXiV preprints
Citation: arXiv:1810.11496 [math.GT]
Date Published: 2018
URL: https://arxiv.org/abs/1810.11496
Registered Mode: imported from a bibtex file
Views: 5939
Created: 30th Jan 2020 at 10:05
Last updated: 5th Mar 2024 at 21:24
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