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Register a new userDrinfeld double for orbifolds
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V. Hinich
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We prove that the Drinfeld double of the category of sheaves on an orbifold is equivalent to the category of sheves on the corresponding inertia orbifold.
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We extend the notion of Hitchin component from surface groups to orbifold groups and prove that this gives new examples of higher Teichm{u}ller spaces. We show that the Hitchin component of an orbifold group is homeomorphic to an open ball and we compute its dimension explicitly. We then give applications to the study of the pressure metric, cyclic Higgs bundles, and the deformation theory of real projective structures on $3$-manifolds.
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