3-dimensional defect TQFTs and their tricategories

Carqueville N, Meusburger C, Schaumann G (2020)

Publication Language: English

Publication Type: Journal article

Publication year: 2020

Journal

Advances in Mathematics Elsevier

Book Volume: 364

Article Number: 107024

URI: https://arxiv.org/abs/1603.01171

DOI: 10.1016/j.aim.2020.107024

Abstract

We initiate a systematic study of 3-dimensional ‘defect’ topological quantum field theories, that we introduce as symmetric monoidal functors on stratified and decorated bordisms. For every such functor we construct a tricategory with duals, which is the natural categorification of a pivotal bicategory. This captures the algebraic essence of defect TQFTs, and it gives precise meaning to the fusion of line and surface defects as well as their duality operations. As examples, we discuss how Reshetikhin-Turaev and Turaev-Viro theories embed into our framework, and how they can be extended to defect TQFTs.

Authors with CRIS profile

Cathérine Meusburger Professur für Mathematik (Darstellungstheorie und Mathematische Physik)

Involved external institutions

Universität Wien / University of Vienna AT Austria (AT) Julius-Maximilians-Universität Würzburg DE Germany (DE)

How to cite

APA:

Carqueville, N., Meusburger, C., & Schaumann, G. (2020). 3-dimensional defect TQFTs and their tricategories. Advances in Mathematics, 364. https://dx.doi.org/10.1016/j.aim.2020.107024

MLA:

Carqueville, Nils, Cathérine Meusburger, and Gregor Schaumann. "3-dimensional defect TQFTs and their tricategories." Advances in Mathematics 364 (2020).

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