Projective twists in A-infinity categories

2011/11/02 by Richard M. Harris, Harris, Richard M. · 1 citation
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1111.0538

openalex publication_date 2011/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a Lagrangian V ≅ CPⁿ in a symplectic manifold (M,ω), there is an associated symplectomorphism ϕ_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 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.

Citations

• Nearby Lagrangians with vanishing Maslov class are homotopy equivalent

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