Transformation Groups Seminar

Speaker: Xin Fu (Ajou University)

"The integral cohomology ring of four-dimensional toric orbifolds"

Time: 09:30

Room: https://westernuniversity.zoom.us/s/93798234275, Passcode: 520011

Toric orbifolds introduced by Davis and Januszkiewicz are topological analogs of projective toric varieties. When a toric orbifold is smooth, its integral cohomology ring is isomorphic to a quotient ring of the Stanley-Reisner ring. Such a formula holds for the singular case over rational coefficients, but integrally it becomes more complicated. For instance, the cohomology of a weighted projective space is additively isomorphic to the cohomology of a complex projective space, but the ring structure differs. In this talk, we focus on toric orbifolds $X$ in four dimensions. If $X$ has a smooth fixed point, we construct a basis for its integral cohomology and present their cup products in a matrix whose entries are explicitly determined by the characteristic function. This is joint work with Tseleung So and Jongbaek Song.