Publikationsserver
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...
Gespeichert in:
| 主要作者: | |
|---|---|
| 其他作者: | |
| 格式: | Dissertation |
| 语言: | 英语 |
| 出版: |
Philipps-Universität Marburg
2018
|
| 主题: | |
| 在线阅读: | PDF-Volltext |
| 标签: |
添加标签
没有标签, 成为第一个标记此记录!
|
| 总结: | 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. |
|---|---|
| 实物描述: | 68 Seiten |
| DOI: | 10.17192/z2018.0496 |