#### Volume 23, issue 2 (2019)

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Orbifolds of $n$–dimensional defect TQFTs

### Nils Carqueville, Ingo Runkel and Gregor Schaumann

Geometry & Topology 23 (2019) 781–864
##### 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 $\mathsc{Z}$, one obtains a new TQFT ${\mathsc{Z}}_{\mathsc{A}}$ by decorating the Poincaré duals of triangulated bordisms with certain algebraic data $\mathsc{A}$ and then evaluating with $\mathsc{Z}$. The orbifold datum $\mathsc{A}$ 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 $n=3$.

##### Keywords
TQFT, orbifold, triangulation-invariance, stratified bordism
Primary: 57R56
##### Publication
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