Projective twists in A-infinity categories

Abstract

Given a Lagrangian V \cong CP^n in a symplectic manifold (M,ω), there is an associated symplectomorphism ϕ_V of M. We define the notion of a CP^n-object in an A-infinity-category A and use this to construct algebraically an A-infinity-functor Φ_V and prove that it induces an autoequivalence of the derived category DA. We conjecture that Φ_V corresponds to the action of ϕ_V and prove this in the lowest dimension n=1. The construction is designed to be mirror to a construction of Huybrechts and Thomas.

19 pages, Version 2: numerous minor corrections

References in corpus (3)

• Derived autoequivalences from periodic algebras
• Exact Lagrangians in plumbings
• Nearby Lagrangians with vanishing Maslov class are homotopy equivalent

Cited by in corpus (3)

• Projective twists and the Hopf correspondence
• Spherical twists and Lagrangian spherical manifolds
• Model projective twists and generalised lantern relations