The cohomology of biquotients via a product on the two-sided bar construction
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2021
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911333658656768 |
|---|---|
| author | Carlson, Jeffrey D. |
| author_facet | Carlson, Jeffrey D. |
| contents | 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-sided bar construction $\mathbf{B}(A',A,A")$ is defined, valid when $A' \leftarrow A \to A"$ is a pair of maps of homotopy Gerstenhaber algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_02986 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The cohomology of biquotients via a product on the two-sided bar construction Carlson, Jeffrey D. Algebraic Topology K-Theory and Homology Rings and Algebras 57T15, 55N91, 57T30, 16E45, 18G55, 55T20 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-sided bar construction $\mathbf{B}(A',A,A")$ is defined, valid when $A' \leftarrow A \to A"$ is a pair of maps of homotopy Gerstenhaber algebras. |
| title | The cohomology of biquotients via a product on the two-sided bar construction |
| topic | Algebraic Topology K-Theory and Homology Rings and Algebras 57T15, 55N91, 57T30, 16E45, 18G55, 55T20 |
| url | https://arxiv.org/abs/2106.02986 |