The Borel Cohomology of Free Iterated Loop Spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
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| _version_ | 1866909995884347392 |
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| author | Levy, Ishan Wu, Justin |
| author_facet | Levy, Ishan Wu, Justin |
| contents | We compute the $\rm{SO}(n+1)$-equivariant mod $2$ Borel cohomology of the free iterated loop space $Z^{S^n}$ when $Z$ is a mod $2$ generalized Eilenberg Mac Lane space. When $n=1$, this recovers Bökstedt and Ottosen's computation for the free loop space. The highlight of our computation is a construction of cohomology classes using an $\mathrm{O}(n)$-equivariant evaluation map and a pushforward map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_13526 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Borel Cohomology of Free Iterated Loop Spaces Levy, Ishan Wu, Justin Algebraic Topology We compute the $\rm{SO}(n+1)$-equivariant mod $2$ Borel cohomology of the free iterated loop space $Z^{S^n}$ when $Z$ is a mod $2$ generalized Eilenberg Mac Lane space. When $n=1$, this recovers Bökstedt and Ottosen's computation for the free loop space. The highlight of our computation is a construction of cohomology classes using an $\mathrm{O}(n)$-equivariant evaluation map and a pushforward map. |
| title | The Borel Cohomology of Free Iterated Loop Spaces |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2105.13526 |