Cohomology of partial quotients | Moscow-Beijing topology seminar

Abstract

Buchstaber and Panov introduced the notion of the moment-angle complex Z. This space isdefined as a union of specific product spaces of discs and circles, equipped with a natural action ofa torus T. Topologically, a moment-angle complex provides a way to understand a simplicial toricvariety through its quotient Z/H, where H is a closed subgroup of T. The computation of thecohomology groups and cup products for these quotient spaces involves technigues fromcombinatorics, algebra, and homotopy theory. These technigues have applications in various fieldsThis talk summarizes known results for computing such cohomology and presents our newprogress. Our new approach uses digraphs to describe the weights that encode how the torus istwisted in the quotient space.