2024/05/08 by Zihong Chen, Chen, Zihong
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2405.05242
openalex publication_date 2024/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with quantum cohomology and Fukaya categories of a closed monotone symplectic manifold X, where we use coefficients in a field k of characteristic p > 0. The main result of this paper is that the quantum Steenrod operations QΣadmit an interpretation in terms of certain operations on the (equivariant) Hochschild invariants of the Fukaya category of X, via suitable (equivariant) versions of the open-closed maps. As an application, we demonstrate how the categorical perspective provides new tools for computing QΣbeyond the reach of known technology. We also explore potential connections of our work to arithmetic homological mirror symmetry.