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Cohomology of partial quotients

组织者

Vassily Manturov , 任世全 , 万喆彦

演讲者

付鑫

时间

2024年06月19日 15:30 至 17:00

地点

A3-2-301

线上

Zoom 831 5020 0580 (141592)

摘要

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.