Divisible convex sets with properly embedded cones by Pierre-Louis Blayac & Gabriele Viaggi ISBN 101007/S1024002400152Y instant download

Divisible convex sets with properly embedded cones by Pierre-Louis Blayac & Gabriele Viaggi ISBN 101007/S1024002400152Y instant download

1. IntroductionIn this article we construct properly convex open subsets  ⊂ RPd divided bysubgroups  < PSLd+1R with special geometric properties in arbitrary dimension d ≥ 3.A properly convex subset  ⊂ RPd is an open subset contained in some affine chartof Rd where it is convex and bounded. It comes with a group of projective symmetriesAut() := A ∈ PSLd+1(R)| A() = and an Aut()-invariant Finsler metric called the Hilbert metric.Discrete and torsion-free subgroups  < Aut() give rise to quotient projectived-manifoldsM := /.Among these groups , of special interest are those such that M = / is compact. Ifsuch discrete subgroup exists, then the convex set  is said divisible and the group  divides. Divisible convex sets are a rich source of geometry, dynamics, and group theory (see[11]).Basic examples are© The Author(s) 2024