Volume 25, issue 7 (2021)

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Codimension-$1$ simplices in divisible convex domains

Martin D Bobb

Geometry & Topology 25 (2021) 3725–3753

Properly embedded simplices in a convex divisible domain Ω Pd 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 (d1)–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.

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geometry, low-dimensional topology, divisible domains, Benoist manifolds, real projective geometry
Mathematical Subject Classification
Primary: 57M50
Secondary: 20H10, 57N16
Received: 22 June 2020
Revised: 17 September 2020
Accepted: 23 October 2020
Published: 25 January 2022
Proposed: Ian Agol
Seconded: David M Fisher, Anna Wienhard
Martin D Bobb
Department of Mathematics
The University of Texas at Austin
Austin, TX
United States
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States