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Projective twists in A-infinity categories (1111.0538v2)
Published 2 Nov 2011 in math.SG and math.KT
Abstract: Given a Lagrangian V \cong CPn in a symplectic manifold (M,\omega), there is an associated symplectomorphism \phi_V of M. We define the notion of a CPn-object in an A-infinity-category A and use this to construct algebraically an A-infinity-functor \Phi_V and prove that it induces an autoequivalence of the derived category DA. We conjecture that \Phi_V corresponds to the action of \phi_V and prove this in the lowest dimension n=1. The construction is designed to be mirror to a construction of Huybrechts and Thomas.
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