The homotopy type of the topological cobordism category
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2018
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| _version_ | 1866910872954208256 |
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| author | Lopez, Mauricio Gomez Kupers, Alexander |
| author_facet | Lopez, Mauricio Gomez Kupers, Alexander |
| contents | We define a cobordism category of topological manifolds and prove that if $d \neq 4$ its classifying space is weakly equivalent to $Ω^{\infty -1} MTTop(d)$, where $MTTop(d)$ is the Thom spectrum of the inverse of the canonical bundle over $BTop(d)$. We also give versions with tangential structures and boundary. The proof uses smoothing theory and excision in the tangential structure to reduce the statement to the computation of the homotopy type of smooth cobordism categories due to Galatius-Madsen-Tillman-Weiss. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_05277 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The homotopy type of the topological cobordism category Lopez, Mauricio Gomez Kupers, Alexander Algebraic Topology Geometric Topology 57N70, 58D05, 55R40 We define a cobordism category of topological manifolds and prove that if $d \neq 4$ its classifying space is weakly equivalent to $Ω^{\infty -1} MTTop(d)$, where $MTTop(d)$ is the Thom spectrum of the inverse of the canonical bundle over $BTop(d)$. We also give versions with tangential structures and boundary. The proof uses smoothing theory and excision in the tangential structure to reduce the statement to the computation of the homotopy type of smooth cobordism categories due to Galatius-Madsen-Tillman-Weiss. |
| title | The homotopy type of the topological cobordism category |
| topic | Algebraic Topology Geometric Topology 57N70, 58D05, 55R40 |
| url | https://arxiv.org/abs/1810.05277 |