Topological Fukaya categories with coefficients

Topological Fukaya categories with coefficients - Tobias Dyckerhoff

Tobias Dyckerhoff
University of Bonn
March 13, 2017
Abstract: Within an emerging approach to Fukaya categories via cohomology with categorical
coefficients, I will outline a theory of a particularly nice class of nonconstant coefficient systems
defined on Riemann surfaces. These are categorical analogues of perverse sheaves, called
perverse schobers. We provide a definition of perverse schobers as categorical sheaves on a
relative two-colored version of the unital Ran space of the surface. We explain how to describe
perverse schobers locally in terms of a paracyclic upgrade of Waldhausen's relative Sconstruction
applied to spherical functors. We conclude, time permitting, with some
applications.