On the homotopy type of L-spectra of the integers
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866913578242539520 |
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| author | Hebestreit, Fabian Land, Markus Nikolaus, Thomas |
| author_facet | Hebestreit, Fabian Land, Markus Nikolaus, Thomas |
| contents | We show that quadratic and symmetric L-theory of the integers are related by Anderson duality and show that both spectra split integrally into the L-theory of the real numbers and a generalised Eilenberg-Mac Lane spectrum. As a consequence, we obtain a corresponding splitting of the space G/Top. Finally, we prove analogous results for the genuine L-spectra recently devised for the study of Grothendieck--Witt theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2004_06889 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the homotopy type of L-spectra of the integers Hebestreit, Fabian Land, Markus Nikolaus, Thomas Algebraic Topology Geometric Topology K-Theory and Homology We show that quadratic and symmetric L-theory of the integers are related by Anderson duality and show that both spectra split integrally into the L-theory of the real numbers and a generalised Eilenberg-Mac Lane spectrum. As a consequence, we obtain a corresponding splitting of the space G/Top. Finally, we prove analogous results for the genuine L-spectra recently devised for the study of Grothendieck--Witt theory. |
| title | On the homotopy type of L-spectra of the integers |
| topic | Algebraic Topology Geometric Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2004.06889 |