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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2019
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/1908.11321 |
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| _version_ | 1866916385048756224 |
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| author | Brantner, Lukas Hahn, Jeremy Knudsen, Ben |
| author_facet | Brantner, Lukas Hahn, Jeremy Knudsen, Ben |
| contents | We construct a spectral sequence converging to the Morava $E$-theory of unordered configuration spaces and identify its E$^2$-page as the homology of a Chevalley-Eilenberg-like complex for Hecke Lie algebras. Based on this, we compute the $E$-theory of the weight $p$ summands of iterated loop spaces of spheres (parametrising the weight $p$ operations on $\mathbb{E}_n$-algebras), as well as the $E$-theory of the configuration spaces of $p$ points on a punctured surface. We read off the corresponding Morava $K$-theory groups, which appear in a conjecture by Ravenel. Finally, we compute the $\mathbb{F}_p$-homology of the space of unordered configurations of $p$ particles on a punctured surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_11321 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The Lubin-Tate Theory of Configuration Spaces: I Brantner, Lukas Hahn, Jeremy Knudsen, Ben Algebraic Topology Geometric Topology 55P35, 55N15, 55N20, 17B56 We construct a spectral sequence converging to the Morava $E$-theory of unordered configuration spaces and identify its E$^2$-page as the homology of a Chevalley-Eilenberg-like complex for Hecke Lie algebras. Based on this, we compute the $E$-theory of the weight $p$ summands of iterated loop spaces of spheres (parametrising the weight $p$ operations on $\mathbb{E}_n$-algebras), as well as the $E$-theory of the configuration spaces of $p$ points on a punctured surface. We read off the corresponding Morava $K$-theory groups, which appear in a conjecture by Ravenel. Finally, we compute the $\mathbb{F}_p$-homology of the space of unordered configurations of $p$ particles on a punctured surface. |
| title | The Lubin-Tate Theory of Configuration Spaces: I |
| topic | Algebraic Topology Geometric Topology 55P35, 55N15, 55N20, 17B56 |
| url | https://arxiv.org/abs/1908.11321 |