Grassmannians and the equivariant cohomology of isotropy actions

Abstract

Recent work of Chen He has determined through GKM methods the Borel equivariant cohomology with rational coefficients of the isotropy action on a real Grassmannian and an real oriented Grassmannian through GKM methods. In this expository note, we propound a less involved approach, due essentially to Vitali Kapovitch, to computing equivariant cohomology rings $H_K^{\ast }(G/H)$ for $G,K,H$ connected Lie groups, and apply it to recover the equivariant cohomology of the Grassmannians. The bulk is setup and commentary; once one believes in the model, the proof itself is under a page.

Updated to match the published version (modulo formatting). Journal ref added. 16 pages

References in corpus (3)

• The cohomology rings of homogeneous spaces
• Equivariant formality of isotropic torus actions
• Equivariant formality of istropy actions

Cited by in corpus (2)

• K-theory and formality
• Localization of equivariant cohomology rings of real Grassmannians