arXiv subjects

Balthazar Fléchelles

Publications and source records attributed to Balthazar Fléchelles.

4 recordsLinked to original sources

arXiv2026

Primitive stability and the Q-conditions for the rank two free group in hyperbolic d-space

The two largest known domains of discontinuity for the action of Out(F_2) on the PSL(2,C)-character variety of F_2 - defined by Minsky's primitive stability, and Bowditch's Q-conditions - were proven to be equal independently by Lee-Xu and Series. We prove the equivalence between primitive stability and a generalization of the Q-conditions for representations of F_2 into the isometry group of hyperbolic d-space for d >= 3, under some assumptions. In particular, these assumptions are satisfied by all W_3-extensible representations. We also generalize Lee-Xu's and Series' results concerning the bounded intersection property to higher dimensions after extending their original definition to this setting.

math.GT↗

arXiv2026

Projective reflection groups of finite covolume

We show that the Coxeter polytopes that have finite volume in their Vinberg domains are exactly the quasiperfect Coxeter polytopes of negative type, i.e. the Coxeter polytopes that are contained in their properly convex Vinberg domain, at the exception of some vertices that are C^1 points of the boundary. As a corollary, we show that for reflection groups à la Vinberg, the Vinberg domain is the only invariant properly convex domain if and only if the action is of finite covolume on the Vinberg domain and the dimension is at least 2.

math.GT↗

arXiv2025

On cusp holonomies in strictly convex projective geometry

We give a complete characterization of the holonomies of strictly convex cusps and of round cusps in convex projective geometry. We build families of generalized cusps of non-maximal rank associated to each strictly convex or round cusp. We also extend Ballas-Cooper-Leitner's definition of generalized cusp to allow for virtually solvable fundamental group, and we produce the first such example with non-virtually nilpotent fundamental group. Along with a companion paper, this allows to build strictly convex cusps and generalized cusps whose fundamental group is any finitely generated virtually nilpotent group. This also has interesting consequences for the theory of relatively Anosov representations.

math.GT↗

arXiv2023

Cubulated hyperbolic groups admit Anosov representations

We prove that any hyperbolic group acting properly discontinuously and cocompactly on a $\mathrm{CAT}(0)$ cube complex admits a projective Anosov representation into $\mathrm{SL}(d, \mathbb{R})$ for some $d$. More specifically, we show that if $Γ$ is a hyperbolic quasiconvex subgroup of a right-angled Coxeter group $C$, then a generic representation of $C$ by reflections restricts to a projective Anosov representation of $Γ$.

math.GR↗