#### Volume 19, issue 2 (2019)

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A note on the $(\infty,n)$–category of cobordisms

### Damien Calaque and Claudia Scheimbauer

Algebraic & Geometric Topology 19 (2019) 533–655
##### Abstract

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 $\left(\infty ,n\right)$–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.

##### Keywords
cobordisms, extended topological field theories, higher categories
##### Mathematical Subject Classification 2010
Primary: 18D05, 57R56
##### Publication
Received: 20 September 2016
Revised: 9 April 2018
Accepted: 26 April 2018
Published: 12 March 2019
##### Authors
 Damien Calaque IMAG Univ Montpellier, CNRS Institut Universitaire de France Montpellier France Claudia Scheimbauer Mathematical Institute University of Oxford Oxford United Kingdom