# Topology Seminar

## The cohomology rings of homogeneous spaces

Matthias Franz, University of Western Ontario

Wednesday, February 12th, 2020
4:00 PM - 5:00 PM
Hylan 1106A

Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $R$. It has been known for a long time that the cohomology of the homogeneous space $G/K$ with coefficients in $R$ and the torsion product of $H^*(BK)$ and $R$ over $H^*(BG)$ are isomorphic as $R$-modules in this case. I will explain that this isomorphism is in fact multiplicative and natural in the pair $(G,K)$ provided that 2 is invertible in $R$. The proof uses homotopy Gerstenhaber algebras in an essential way.

Event contact: samelott at ur dot rochester dot edu