Volume 19, issue 2 (2019)

 Recent Issues
Author Index
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 To Appear Other MSP Journals
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