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- W3216652197 abstract "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 $k$. It is known that in this case the cohomology of the homogeneous space $G/K$ with coefficients in $k$ and the torsion product of $H^{*}(BK)$ and $k$ over $H^{*}(BG)$ are isomorphic as $k$-modules. We show that this isomorphism is multiplicative and natural in the pair $(G,K)$ provided that 2 is invertible in $k$. The proof uses homotopy Gerstenhaber algebras in an essential way. In particular, we show that the normalized singular cochains on the classifying space of a torus are formal as a homotopy Gerstenhaber algebra." @default.
- W3216652197 created "2021-12-06" @default.
- W3216652197 creator A5012844162 @default.
- W3216652197 date "2021-11-22" @default.
- W3216652197 modified "2023-09-24" @default.
- W3216652197 title "The cohomology rings of homogeneous spaces" @default.
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- W3216652197 doi "https://doi.org/10.1112/topo.12213" @default.
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