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Titel:On the equivariant cohomology of isotropy actions
Autor:Hagh Shenas Noshari, Sam
Weitere Beteiligte: Goertsches, Oliver (Prof. Dr.)
URN: urn:nbn:de:hebis:04-z2018-04969
DDC: Mathematik


Äquivariante Kohomologietheorie, Differentialgeometrie, Symmetric space, equivariant cohomology, Lie-Gruppe, cohomology, Symmetrischer Raum, differential geometry, Lie-Algebra, Kohomologie, Lie group, Lie algebra

Let G be a compact connected Lie group and K \subseteq G a closed subgroup. We show that the isotropy action of K on G/K is equivariantly formal and that the space G/K is formal in the sense of rational homotopy theory whenever K is the identity component of the intersection of the fixed point sets of two distinct involutions on G, so that G/K is a \mathbb{Z}_2\times\mathbb{Z}_2--symmetric space. If K is the identity component of the fixed point set of a single involution and H \subseteq G is a closed connected subgroup containing K, then we show that the action of K on G/H by left-multiplication is equivariantly formal. The latter statement follows from the well-known special case K = H, but is proved by different means, namely by providing an algebraic model for the equivariant cohomology of certain actions.

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