Geodesic
The homotopy type of the topological cobordism category
Documenta mathematica, Tome 27 (2022), pp. 2107-2182 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

We define a cobordism category of topological manifolds and prove that if d=4 its classifying space is weakly equivalent to Ω∞−1MTTop(d), where MTTop(d) is the Thom spectrum of the inverse of the canonical bundle over BTop(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.
DOI : 10.4171/dm/x27
Classification : 55R40, 57N70, 58D05
Mots-clés : cobordism categories, topological manifolds 
@article{10_4171_dm_x27,
     author = {Mauricio Gomez Lopez and Alexander Kupers},
     title = {The homotopy type of the topological cobordism category},
     journal = {Documenta mathematica},
     pages = {2107--2182},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x27},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x27/}
}
TY  - JOUR
AU  - Mauricio Gomez Lopez
AU  - Alexander Kupers
TI  - The homotopy type of the topological cobordism category
JO  - Documenta mathematica
PY  - 2022
SP  - 2107
EP  - 2182
VL  - 27
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/x27/
DO  - 10.4171/dm/x27
ID  - 10_4171_dm_x27
ER  - 
%0 Journal Article
%A Mauricio Gomez Lopez
%A Alexander Kupers
%T The homotopy type of the topological cobordism category
%J Documenta mathematica
%D 2022
%P 2107-2182
%V 27
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/x27/
%R 10.4171/dm/x27
%F 10_4171_dm_x27
Mauricio Gomez Lopez; Alexander Kupers. The homotopy type of the topological cobordism category. Documenta mathematica, Tome 27 (2022), pp. 2107-2182. doi: 10.4171/dm/x27

Cité par Sources :