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BIMSA Topology Seminar
The algebraic structure of cohomology of 4-dimensional toric orbifolds
The algebraic structure of cohomology of 4-dimensional toric orbifolds
Organizers
Speaker
Larry So
Time
Thursday, February 27, 2025 2:30 PM - 3:30 PM
Venue
A3-4-301
Online
Zoom 204 323 0165
(BIMSA)
Abstract
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.