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Orbifold graph TQFTs

Autor(en)
Nils Carqueville, Vincentas Mulevicius, Ingo Runkel, Gregor Schaumann, Daniel Scherl
Abstrakt

A generalised orbifold of a defect TQFT $\mathcal{Z}$ is another TQFT $\mathcal{Z}_{\mathcal{A}}$ obtained by performing a state sum construction internal to $\mathcal{Z}$. As an input it needs a so-called orbifold datum $\mathcal{A}$ which is used to label stratifications coming from duals of triangulations and is subject to conditions encoding the invariance under Pachner moves. In this paper we extend the construction of generalised orbifolds of $3$-dimensional TQFTs to include line defects. The result is a TQFT acting on 3-bordisms with embedded ribbon graphs labelled by a ribbon category $\mathcal{W}_{\mathcal{A}}$ that we canonically associate to $\mathcal{Z}$ and $\mathcal{A}$. We also show that for special orbifold data, the internal state sum construction can be performed on more general skeletons than those dual to triangulations. This makes computations with $\mathcal{Z}_{\mathcal{A}}$ easier to handle in specific examples.

Organisation(en)
Mathematische Physik
Externe Organisation(en)
Universität Hamburg, Julius-Maximilians-Universität Würzburg
Anzahl der Seiten
67
Publikationsdatum
01-2021
ÖFOS 2012
103019 Mathematische Physik
Schlagwörter
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/19908bbf-7384-4607-8328-fa0c7a410699