Sur la division des domaines de Siegel

Vey, Jacques

doi:10.24033/asens.1200

Cited by 18 publications

(19 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is a theorem of Vey from 1970 which rules out the case where Ω is completely foliated by flats [Vey70]. Recall that a linear group Γ is said to act strongly irreducibly if every finite index subgroup Γ < Γ acts irreducibly.…”

Section: Discreteness Of Fmentioning

confidence: 99%

See 1 more Smart Citation

Codimension-$1$ Simplices in Divisible Convex Domains

Bobb

2020

Preprint

View full text Add to dashboard Cite

Properly embedded simplices in a convex divisible domain Ω ⊂ RP d behave somewhat like flats in Riemannian manifolds [Sch90], so we call them flats. We show that the set of codimension-1 flats has image which is a finite collection of disjoint virtual (d − 1)-tori in the compact quotient manifold. If this collection of virtual tori is non-empty, then the components of its complement are cusped convex projective manifolds with type d cusps.

show abstract

Section: Discreteness Of Fmentioning

confidence: 99%

“…Theorem 4.7 (Vey irreducibility). [Vey70] If Ω is irreducible, then Γ acts strongly irreducibly on R d+1 . This allows us to conclude the following.…”

Section: Discreteness Of Fmentioning

confidence: 99%

Codimension-$1$ Simplices in Divisible Convex Domains

Bobb

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Theorem 3.12 (Vey, [86]). Let Γ be a discrete subgroup of SL d+1 (R) that divides a properly convex open set Ω.…”

Section: The Following Question Is Then Natural and Openmentioning

confidence: 99%

Around groups in Hilbert geometry

Marquis

2014

IRMA Lectures in Mathematics and Theoretical Physics

View full text Add to dashboard Cite

The main goal of this chapter is to study the groupwhere Ω is a properly convex open set of P d . The following fact is very basic and also very useful.Proposition 1.1. The action of the group Coll ± (Ω) on Ω is by isometries for the Hilbert distance. Consequently, the action of Coll ± (Ω) on Ω is proper, so Coll ± (Ω) is a closed subgroup of PGL d+1 (R) and so is a Lie group. 7 A hyperplane H is a supporting hyperplane at p ∈ ∂Ω when H ∩ Ω = ∅ and p ∈ H.

show abstract

“…While this sounds very general, there are few such examples known aside from bounded symmetric domains [22]. The results of Frankel [10], Vey [28] and Wong [29] show that under various additional restrictions, such a U is necessarily a bounded symmetric domain (see [15] for a survey of closely related results). From our point of view, this leads to the following problem.…”

Section: Open Problemsmentioning

confidence: 99%