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Codimension-1 Flats in Compact Convex Projective Manifolds

Random and Arithmetic Structures in Topology: Introductory Workshop August 25, 2020 - September 11, 2020

September 11, 2020 (10:30 AM PDT - 11:30 AM PDT)
Speaker(s): Martin Bobb (University of Michigan)
Location: SLMath: Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Codimension-1 Flats In Compact Convex Projective Manifolds

Abstract

In real convex projective geometry, simplices have many characteristics of flat geometry. In particular, we will discuss compact convex projective manifolds (in any dimension greater than 2) which have properly embedded codimension-1 simplices, and demonstrate that examining these submanifolds yields strong topological data about the total manifold. This work generalizes a 2006 theorem of Benoist for compact 3-dimensional convex projective manifolds which gives a JSJ decomposition along properly embedded triangles. 

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Codimension-1 Flats In Compact Convex Projective Manifolds

H.264 Video 1003_28797_8496_Codimension-1_Flats_in_Compact_Convex_Projective_Manifolds.mp4
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