The Lubin–Tate theory of configuration spaces: I
We construct a spectral sequence converging to the Lubin–Tate theory, that is, Morava <em>E</em>-theory, of unordered configuration spaces and identify its E<sup>2</sup>-page as the homology of a Chevalley–Eilenberg-like complex for Hecke Lie algebras. Based on this, we comp...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Wiley
2024
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| _version_ | 1817931388364521472 |
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| author | Brantner, L Hahn, J Knudsen, B |
| author_facet | Brantner, L Hahn, J Knudsen, B |
| author_sort | Brantner, L |
| collection | OXFORD |
| description | We construct a spectral sequence converging to the Lubin–Tate theory, that is, Morava <em>E</em>-theory, of unordered configuration spaces and identify its E<sup>2</sup>-page as the homology of a Chevalley–Eilenberg-like complex for Hecke Lie algebras. Based on this, we compute the <em>E</em>-theory of the weight <em>p</em> summands of iterated loop spaces of spheres (parametrising the weight <em>p</em> operations on 𝔼<sub><em>n</em></sub>-algebras), as well as the <em>E</em>-theory of the configuration spaces of <em>p</em> points on a punctured surface. We read off the corresponding Morava <em>K</em>-theory groups, which appear in a conjecture by Ravenel. Finally, we compute the 𝔽<sub><em>p</em></sub>-homology of the space of unordered configurations of <em>p</em> particles on a punctured surface. |
| first_indexed | 2024-09-25T04:33:32Z |
| format | Journal article |
| id | oxford-uuid:7512cc64-07a5-4223-8f87-5c1a967ac950 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:21:14Z |
| publishDate | 2024 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:7512cc64-07a5-4223-8f87-5c1a967ac9502024-11-12T12:27:58ZThe Lubin–Tate theory of configuration spaces: IJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7512cc64-07a5-4223-8f87-5c1a967ac950EnglishSymplectic ElementsWiley2024Brantner, LHahn, JKnudsen, BWe construct a spectral sequence converging to the Lubin–Tate theory, that is, Morava <em>E</em>-theory, of unordered configuration spaces and identify its E<sup>2</sup>-page as the homology of a Chevalley–Eilenberg-like complex for Hecke Lie algebras. Based on this, we compute the <em>E</em>-theory of the weight <em>p</em> summands of iterated loop spaces of spheres (parametrising the weight <em>p</em> operations on 𝔼<sub><em>n</em></sub>-algebras), as well as the <em>E</em>-theory of the configuration spaces of <em>p</em> points on a punctured surface. We read off the corresponding Morava <em>K</em>-theory groups, which appear in a conjecture by Ravenel. Finally, we compute the 𝔽<sub><em>p</em></sub>-homology of the space of unordered configurations of <em>p</em> particles on a punctured surface. |
| spellingShingle | Brantner, L Hahn, J Knudsen, B The Lubin–Tate theory of configuration spaces: I |
| title | The Lubin–Tate theory of configuration spaces: I |
| title_full | The Lubin–Tate theory of configuration spaces: I |
| title_fullStr | The Lubin–Tate theory of configuration spaces: I |
| title_full_unstemmed | The Lubin–Tate theory of configuration spaces: I |
| title_short | The Lubin–Tate theory of configuration spaces: I |
| title_sort | lubin tate theory of configuration spaces i |
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