English

Projective twists in A-infinity categories

Symplectic Geometry 2012-03-29 v2 K-Theory and Homology

Abstract

Given a Lagrangian V \cong CP^n in a symplectic manifold (M,\omega), there is an associated symplectomorphism \phi_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 \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.

Keywords

Cite

@article{arxiv.1111.0538,
  title  = {Projective twists in A-infinity categories},
  author = {Richard M. Harris},
  journal= {arXiv preprint arXiv:1111.0538},
  year   = {2012}
}

Comments

19 pages, Version 2: numerous minor corrections

R2 v1 2026-06-21T19:29:46.735Z