Divisible convex sets with properly embedded cones

Blayac, Pierre-Louis; Viaggi, Gabriele

doi:10.48550/arxiv.2302.07177

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Nonstrictly Convex Divisible Examples1

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2023

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“…More recently, Blayac-Viaggi [8] have constructed additional examples of irreducible nonstrictly convex divisible domains in ℙ(ℝ 𝑑 ), for any dimension 𝑑 ⩾ 4. The construction does not use reflection groups, but rather a combination of arithmetic methods and a procedure known as projective bending.…”

Section: Nonstrictly Convex Divisible Examplesmentioning

confidence: 99%

Dynamical properties of convex cocompact actions in projective space

Weisman

2023

Journal of Topology

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We give a dynamical characterization of convex cocompact group actions on properly convex domains in projective space in the sense of Danciger–Guéritaud–Kassel: we show that convex cocompactness in is equivalent to an expansion property of the group about its limit set, occurring in different Grassmannians. As an application, we give a sufficient and necessary condition for convex cocompactness for groups that are hyperbolic relative to a collection of convex cocompact subgroups. We show that convex cocompactness in this situation is equivalent to the existence of an equivariant homeomorphism from the Bowditch boundary to the quotient of the limit set of the group by the limit sets of its peripheral subgroups.

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Section: Nonstrictly Convex Divisible Examplesmentioning

confidence: 99%

Dynamical properties of convex cocompact actions in projective space

Weisman

2023

Journal of Topology

View full text Add to dashboard Cite

show abstract

Divisible convex sets with properly embedded cones

Cited by 1 publication

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Dynamical properties of convex cocompact actions in projective space

Dynamical properties of convex cocompact actions in projective space

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