• Corpus ID: 235358921

The cohomology of biquotients via a product on the two-sided bar construction (expository version)

  title={The cohomology of biquotients via a product on the two-sided bar construction (expository version)},
  author={Jeffrey D. Carlson},
  journal={arXiv: Algebraic Topology},
  • J. Carlson
  • Published 5 June 2021
  • Mathematics
  • arXiv: Algebraic Topology
We compute the Borel equivariant cohomology ring of the left $K$-action on a homogeneous space $G/H$, where $G$ is a connected Lie group, $H$ and $K$ are closed, connected subgroups and $2$ and the torsion primes of the Lie groups are units of the coefficient ring. As a special case, this gives the singular cohomology rings of biquotients $H \backslash G / K$. This depends on a version of the Eilenberg-Moore theorem developed in the appendix, where a novel multiplicative structure on the two… 
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