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Codimension-$1$ simplices
in divisible convex domains
Martin D Bobb |
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Geometry & Topology 25 (2021) 3725–3753
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Abstract |
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Properly embedded simplices in a convex divisible domain 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- flats has image which is a finite collection of disjoint virtual –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 cusps. |
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Keywords
geometry, low-dimensional topology, divisible domains,
Benoist manifolds, real projective geometry
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Mathematical Subject Classification
Primary: 57M50
Secondary: 20H10, 57N16
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References |
Publication
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
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Authors |
| 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 |
