Cohomology of partial quotients
Organizers
Vassily Manturov
, Shiquan Ren
,
Zhe Yan Wan
Speaker
Time
Wednesday, June 19, 2024 3:30 PM - 5:00 PM
Venue
A3-2-301
Online
Zoom 831 5020 0580
(141592)
Abstract
Buchstaber and Panov introduced the notion of the moment-angle complex Z. This space is defined as a union of specific product spaces of discs and circles, equipped with a natural action of a torus T. Topologically, a moment-angle complex provides a way to understand a simplicial toric variety through its quotient Z/H, where H is a closed subgroup of T. The computation of the cohomology groups and cup products for these quotient spaces involves techniques from combinatorics, algebra, and homotopy theory. These techniques have applications in various fields. This talk summarizes known results for computing such cohomology and presents our new progress. Our new approach uses digraphs to describe the weights that encode how the torus is twisted in the quotient space.