On the equivariant cohomology of isotropy actions
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...
Gardado en:
Autor Principal: | |
---|---|
Outros autores: | |
Formato: | Dissertation |
Idioma: | inglés |
Publicado: |
Philipps-Universität Marburg
2018
|
Schlagworte: | |
Acceso en liña: | Texto completo PDF |
Tags: |
Engadir etiqueta
Sen Etiquetas, Sexa o primeiro en etiquetar este rexistro!
|
Zusammenfassung: | 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. |
---|---|
Descrición Física: | 68 Seiten |
DOI: | 10.17192/z2018.0496 |