Abstract: Convex projective structures on manifolds are a rich generalization of hyperbolic structures. One key difference is that a convex projective manifold may have flat substructures. We will discuss some first examples of convex projective geometry, and then describe a natural decomposition of compact convex manifolds along their codimension-1 flats. This generalizes a result of Benoist, which states that a compact convex projective 3-manifold geometrically JSJ-decomposes into cusped hyperbolic manifolds.
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