Geodesic
A note on the (∞,n)–category of cobordisms
Calaque, Damien1 ; Scheimbauer, Claudia2
1 IMAG, Univ Montpellier, CNRS, Institut Universitaire de France, Montpellier, France
2 Mathematical Institute, University of Oxford, Oxford, United Kingdom
Algebraic and Geometric Topology, Tome 19 (2019) no. 2, pp. 533-655

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

In this extended note we give a precise definition of fully extended topological field theories à la Lurie. Using complete n–fold Segal spaces as a model, we construct an (∞,n)–category of n–dimensional bordisms, possibly with tangential structure. We endow it with a symmetric monoidal structure and show that we can recover the usual category of bordisms.

DOI : 10.2140/agt.2019.19.533
Classification : 18D05, 57R56
Keywords: cobordisms, extended topological field theories, higher categories

Calaque, Damien 1 ; Scheimbauer, Claudia 2

1 IMAG, Univ Montpellier, CNRS, Institut Universitaire de France, Montpellier, France
2 Mathematical Institute, University of Oxford, Oxford, United Kingdom 
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Calaque, Damien; Scheimbauer, Claudia. A note on the (∞,n)–category of cobordisms. Algebraic and Geometric Topology, Tome 19 (2019) no. 2, pp. 533-655. doi: 10.2140/agt.2019.19.533

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