Convex projective manifolds are a generalization of hyperbolic manifolds. Koszul
showed that the set of holonomies of convex projective structures on a compact
manifold is open in the representation variety. We will describe an extension of this
result to convex projective manifolds whose ends are generalized cusps, due to
Cooper-Long-Tillmann. Generalized cusps are certain ends of convex projective
manifolds. They may contain both hyperbolic and parabolic elements. We will describe
their classification (due to Ballas-Cooper-Leitner), and explain how generalized cusps
turn out to be deformations of cusps of hyperbolic manifolds. We will also explore
the moduli space of generalized cusps, it is a semi-algebraic set of dimension n^2-n,
contractible, and may be studied using several different invariants. For the case of
three manifolds, the moduli space is homeomorphic to R^2 times a cone on a solid
torus.
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