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Orbifolds of
$n$–dimensional defect TQFTs
Nils Carqueville, Ingo Runkel and Gregor Schaumann |
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Geometry & Topology 23 (2019) 781–864
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Abstract |
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We introduce the notion of –dimensional topological quantum field theory (TQFT) with defects as a symmetric monoidal functor on decorated stratified bordisms of dimension . The familiar closed or open–closed TQFTs are special cases of defect TQFTs, and for and our general definition recovers what had previously been studied in the literature. Our main construction is that of “generalised orbifolds” for any –dimensional defect TQFT: Given a defect TQFT , one obtains a new TQFT by decorating the Poincaré duals of triangulated bordisms with certain algebraic data and then evaluating with . The orbifold datum is constrained by demanding invariance under –dimensional Pachner moves. This procedure generalises both state sum models and gauging of finite symmetry groups for any . After developing the general theory, we focus on the case . |
Keywords
TQFT, orbifold, triangulation-invariance, stratified
bordism
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Mathematical Subject Classification 2010
Primary: 57R56
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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
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Authors |
| Nils Carqueville | |
| Fakultät für Mathematik Universität Wien Wien Austria |
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| Ingo Runkel | |
| Fachbereich Mathematik Universität Hamburg Hamburg Germany |
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| Gregor Schaumann | |
| Fakultät für Mathematik Universität Wien Wien Austria |
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