A note on the (∞,n)–category of cobordisms

Calaque, Damien; Scheimbauer, Claudia

doi:10.2140/agt.2019.19.533

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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

DOI: 10.2140/agt.2019.19.533

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 $(\infty, n)$ –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

Volume 19, issue 2 (2019)