Codimension-1 simplices in divisible convex domains

Bobb, Martin D¹

¹ Department of Mathematics, The University of Texas at Austin, Austin, TX, United States, Department of Mathematics, University of Michigan, Ann Arbor, MI, United States

Geometry & topology, Tome 25 (2021) no. 7, pp. 3725-3753.

Résumé

Properly embedded simplices in a convex divisible domain $\Omega \subset ℝP^d$ behave somewhat like flats in Riemannian manifolds (Geom. Dedicata 33 (1990) 251–263), so we call them flats. We show that the set of codimension-$1$ flats has image which is a finite collection of disjoint virtual $\left(d-1\right)$–tori in the compact quotient manifold. If this collection of virtual tori is nonempty, then the components of its complement are cusped convex projective manifolds with type $d$ cusps.

Détail

DOI : 10.2140/gt.2021.25.3725

Keywords: geometry, low-dimensional topology, divisible domains, Benoist manifolds, real projective geometry

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