2015/12/14 by Amitai Netser Zernik, Zernik, Amitai Netser
Mathematics · Physics and Astronomy · #53D12 14J 55N91 57T30 55N25 16E99 (Secondary) #53D37 53D45 (Primary) #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1512.04507
openalex publication_date 2015/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We set up an algebraic framework for the study of pseudoholomorphic discs bounding nonorientable Lagrangians, as well as equivariant extensions of such structures arising from a torus action. First, we define unital cyclic twisted A_∞ algebras and prove some basic results about them, including a homological perturbation lemma which allows one to construct minimal models of such algebras. We then construct an equivariant extension of A_∞ algebras which are invariant under a torus action on the underlying complex. Finally, we construct a homotopy retraction of the Cartan-Weil complex to equivariant cohomology, which allows us to construct minimal models for equivariant cyclic twisted A_∞ algebras. In a forthcoming paper we will use these results to define and obtain fixed-point expressions for the open Gromov-Witten theory of \mathbbRP2n \hookrightarrow \mathbbCP2n, as well as its equivariant extension.