Twisted actions on cohomologies and bimodules
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908140222545920 |
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| author | Shchigolev, Vladimir |
| author_facet | Shchigolev, Vladimir |
| contents | We introduce a twisted action of the equivariant cohomology of the singleton $H_R^\bullet({\rm pt},\Bbbk)$ on the equivarinat cohomology $H_L^\bullet(X,\Bbbk)$ of an $L$-space $X$. Considering this actions as a right action, $H_L^\bullet(X,\Bbbk)$ becomes a bimodule togeather with the canonical left action of $H_L^\bullet({\rm pt},\Bbbk)$. Using this bimodule structure, we prove an equivariant version of the Künneth isomorphism.
We apply this result to the computation of the equivariant cohomologies of Bott-Samelson varieties and to a geometric construction of the bimodule morphisms between these cohomologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_10745 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Twisted actions on cohomologies and bimodules Shchigolev, Vladimir Algebraic Topology Representation Theory 55N25 We introduce a twisted action of the equivariant cohomology of the singleton $H_R^\bullet({\rm pt},\Bbbk)$ on the equivarinat cohomology $H_L^\bullet(X,\Bbbk)$ of an $L$-space $X$. Considering this actions as a right action, $H_L^\bullet(X,\Bbbk)$ becomes a bimodule togeather with the canonical left action of $H_L^\bullet({\rm pt},\Bbbk)$. Using this bimodule structure, we prove an equivariant version of the Künneth isomorphism. We apply this result to the computation of the equivariant cohomologies of Bott-Samelson varieties and to a geometric construction of the bimodule morphisms between these cohomologies. |
| title | Twisted actions on cohomologies and bimodules |
| topic | Algebraic Topology Representation Theory 55N25 |
| url | https://arxiv.org/abs/2301.10745 |