Geodesic
The homotopy type of the topological cobordism category
Documenta mathematica, Tome 27 (2022), pp. 2107-2182.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We define a cobordism category of topological manifolds and prove that if $d\neq 4$ its classifying space is weakly equivalent to $\Omega^{\infty -1}MT\mathrm{Top}(d)$, where $MT\mathrm{Top}(d)$ is the Thom spectrum of the inverse of the canonical bundle over $B\mathrm{Top}(d)$. We also give versions for manifolds with tangential structures and/or 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.
Classification : 57N70, 58D05, 55R40
Keywords: cobordism categories, topological manifolds 
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     author = {Gomez Lopez, Mauricio and Kupers, Alexander},
     title = {The homotopy type of the topological cobordism category},
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     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a12/}
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Gomez Lopez, Mauricio; Kupers, Alexander. The homotopy type of the topological cobordism category. Documenta mathematica, Tome 27 (2022), pp. 2107-2182. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a12/