Global model categories and topological André-Quillen cohomology
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917768628011008 |
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| author | Lenz, Tobias Stahlhauer, Michael |
| author_facet | Lenz, Tobias Stahlhauer, Michael |
| contents | We introduce global model categories as a general framework to capture several phenomena in global equivariant homotopy theory. We then construct genuine stabilizations of these, generalizing the usual passage from unstable to stable global homotopy theory. Finally, we define the global topological André-Quillen cohomology of an ultra-commutative ring spectrum and express it in terms of a genuine stabilization in our framework in analogy with the classical non-equivariant description obtained by Basterra and Mandell. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06207 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global model categories and topological André-Quillen cohomology Lenz, Tobias Stahlhauer, Michael Algebraic Topology 55P91, 55P43 (Primary) 18N40, 55U35 (Secondary) We introduce global model categories as a general framework to capture several phenomena in global equivariant homotopy theory. We then construct genuine stabilizations of these, generalizing the usual passage from unstable to stable global homotopy theory. Finally, we define the global topological André-Quillen cohomology of an ultra-commutative ring spectrum and express it in terms of a genuine stabilization in our framework in analogy with the classical non-equivariant description obtained by Basterra and Mandell. |
| title | Global model categories and topological André-Quillen cohomology |
| topic | Algebraic Topology 55P91, 55P43 (Primary) 18N40, 55U35 (Secondary) |
| url | https://arxiv.org/abs/2302.06207 |