2023/11/28 by Christ, Merlin · 3 citations
#18N60 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2311.16597
We give a treatment of relative Calabi--Yau structures on functors between R-linear stable ∞-categories, with R any 𝔼_∞-ring spectrum, generalizing previous treatments in the setting of dg-categories. Using their gluing properties, we further construct relative Calabi--Yau structures on the global sections of perverse schobers, i.e. categorified perverse sheaves, on surfaces with boundary. We treat examples related to Fukaya categories and representation theory. In a related direction, we define the monodromy of a perverse schober parametrized by a ribbon graph on a framed surface and show that it forms a local system of stable ∞-categories.