A simple universal property of Thom ring spectra
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2014
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| _version_ | 1866914228685766656 |
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| author | Antolín-Camarena, Omar Barthel, Tobias |
| author_facet | Antolín-Camarena, Omar Barthel, Tobias |
| contents | We give a simple universal property of the multiplicative structure on the Thom spectrum of an $n$-fold loop map, obtained as a special case of a characterization of the algebra structure on the colimit of a lax $\mathcal{O}$-monoidal functor. This allows us to relate Thom spectra to $\mathbb{E}_n$-algebras of a given characteristic in the sense of Szymik. As applications, we recover the Hopkins--Mahowald theorem realizing $H\mathbb{F}_p$ and $H\mathbb{Z}$ as Thom spectra, and compute the topological Hochschild homology and the cotangent complex of various Thom spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1411_7988 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | A simple universal property of Thom ring spectra Antolín-Camarena, Omar Barthel, Tobias Algebraic Topology 55N20, 55P42, 55P43, 55P48 We give a simple universal property of the multiplicative structure on the Thom spectrum of an $n$-fold loop map, obtained as a special case of a characterization of the algebra structure on the colimit of a lax $\mathcal{O}$-monoidal functor. This allows us to relate Thom spectra to $\mathbb{E}_n$-algebras of a given characteristic in the sense of Szymik. As applications, we recover the Hopkins--Mahowald theorem realizing $H\mathbb{F}_p$ and $H\mathbb{Z}$ as Thom spectra, and compute the topological Hochschild homology and the cotangent complex of various Thom spectra. |
| title | A simple universal property of Thom ring spectra |
| topic | Algebraic Topology 55N20, 55P42, 55P43, 55P48 |
| url | https://arxiv.org/abs/1411.7988 |