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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 (,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.

Keywords
cobordisms, extended topological field theories, higher categories
Mathematical Subject Classification 2010
Primary: 18D05, 57R56
References
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