Mathematics Colloquia and Seminars

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A real projective structure on a manifold or an orbifold is given by locally modeling the space by pieces of real projective space glued with projective patching maps. Hyperbolic manifolds are examples. In this talk, we will give some survey of results for deformation spaces for closed manifolds and orbifolds. A generalization Weil’s work shows that the deformation spaces of convex real projective structures on closed manifolds or orbifolds are usually open and closed in the PGL(n+1, R)-character varieties. We will aim to prove the openness and closeness for the deformation spaces of convex real projective structures on orbifolds with ends satisfying certain conditions. (Cooper, Long, and Tillman are also considering structures with analogous types of ends.)