2011/11/06 by Daniel Pomerleano, Pomerleano, Daniel
Mathematics · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1111.1460
openalex publication_date 2011/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a simply connected manifold M such that its cochain algebra, C^⋆(M), is a pure Sullivan dga, this paper considers curved deformations of the algebra C_⋆(ΩM) and consider when the category of curved modules over these algebras becomes fully dualizable. For simple manifolds, like products of spheres, we are able to give an explicit criterion for when the resulting category of curved modules is smooth, proper and CY and thus gives rise to a TQFT. We give Floer theoretic interpretations of these theories for projective spaces and their products, which involve defining a Fukaya category which counts holomorphic disks with prescribed tangencies to a divisor.