BIMSA >
BIMSA Topology Seminar
The algebraic structure of cohomology of 4-dimensional toric orbifolds
The algebraic structure of cohomology of 4-dimensional toric orbifolds
演讲者
Larry So
时间
2025年02月27日 14:30 至 15:30
地点
A3-4-301
线上
Zoom 204 323 0165
(BIMSA)
摘要
A toric orbifold $X$ is characterized by a simple polytope $P$ and a characteristic function $\lambda$. A fundamental problem is to understand the relationship between the topology of $X$, the combinatorial data of the pair $(P,\lambda)$, and the algebraic structure of its cohomology $H^*(X)$.
In this talk, I will present a formula that expresses cup products in the cohomology of a 4-dimensional toric orbifold $X$ in terms of the pair $(P,\lambda)$. Notably, when $X$ is a toric surface, this formula recovers the "dual" of the intersection form from Intersection Theory. In addition, this leads to a criterion for the triviality of Steenrod operations on the cohomology of $X$, which allows us to extract topological information about $X$.
This talk is based on joint work with Xin Fu and Songbaek Song.
In this talk, I will present a formula that expresses cup products in the cohomology of a 4-dimensional toric orbifold $X$ in terms of the pair $(P,\lambda)$. Notably, when $X$ is a toric surface, this formula recovers the "dual" of the intersection form from Intersection Theory. In addition, this leads to a criterion for the triviality of Steenrod operations on the cohomology of $X$, which allows us to extract topological information about $X$.
This talk is based on joint work with Xin Fu and Songbaek Song.