Projective twists in A-infinity categories
Abstract
Given a Lagrangian V CPn in a symplectic manifold (M,ω), there is an associated symplectomorphism φV 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 V and prove that it induces an autoequivalence of the derived category DA. We conjecture that V corresponds to the action of φV 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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