Orbifolds of n–dimensional defect TQFTs

Carqueville, Nils; Runkel, Ingo; Schaumann, Gregor

doi:10.2140/gt.2019.23.781

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

This article is available for purchase or by subscription. See below.

Orbifolds of $n$–dimensional defect TQFTs

Nils Carqueville, Ingo Runkel and Gregor Schaumann

Geometry & Topology 23 (2019) 781–864

DOI: 10.2140/gt.2019.23.781

Abstract

We introduce the notion of $n$ –dimensional topological quantum field theory (TQFT) with defects as a symmetric monoidal functor on decorated stratified bordisms of dimension $n$ . The familiar closed or open–closed TQFTs are special cases of defect TQFTs, and for $n = 2$ and $n = 3$ our general definition recovers what had previously been studied in the literature.

Our main construction is that of “generalised orbifolds” for any $n$ –dimensional defect TQFT: Given a defect TQFT $Z$ , one obtains a new TQFT $Z_{A}$ by decorating the Poincaré duals of triangulated bordisms with certain algebraic data $A$ and then evaluating with $Z$ . The orbifold datum $A$ is constrained by demanding invariance under $n$ –dimensional Pachner moves. This procedure generalises both state sum models and gauging of finite symmetry groups for any $n$ . After developing the general theory, we focus on the case $n = 3$ .

PDF Access Denied

We have not been able to recognize your IP address 18.191.88.249 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

TQFT, orbifold, triangulation-invariance, stratified bordism

Mathematical Subject Classification 2010

Primary: 57R56

References

Publication

Received: 20 August 2017

Revised: 3 November 2017

Accepted: 12 May 2018

Published: 8 April 2019

Proposed: Peter Teichner

Seconded: Stefan Schwede, Ralph Cohen

Authors

Nils Carqueville
Fakultät für Mathematik Universität Wien Wien Austria

Ingo Runkel
Fachbereich Mathematik Universität Hamburg Hamburg Germany

Gregor Schaumann
Fakultät für Mathematik Universität Wien Wien Austria

Volume 23, issue 2 (2019)