A geometrical description of untwisted 3d Dijkgraaf-Witten TQFT with defects
Faria Martins J, Meusburger C (2026)
Publication Type: Journal article
Publication year: 2026
Journal
Book Volume: 494
Article Number: 110923
DOI: 10.1016/j.aim.2026.110923
Abstract
We give a simple, geometric and explicit construction of 3d untwisted Dijkgraaf-Witten theory with defects of all codimensions. It is given as a symmetric monoidal functor from a defect cobordism category into the category of finite-dimensional complex vector spaces. The objects of this category are oriented stratified surfaces and its morphisms are equivalence classes of stratified cobordisms, both labelled with higher categorical data. This TQFT is constructed in terms of geometric quantities such as fundamental groupoids and bundles and requires neither state sums on triangulations nor diagrammatic calculi for higher categories. It is obtained from a functor that assigns to each defect surface a representation of a gauge groupoid and to each defect cobordism a fibrant span of groupoids and an intertwiner between the groupoid representations at its boundary. It is constructed by homotopy theoretic methods and allows for an explicit computation of examples. In particular, we show how the 2d part of this defect TQFT gives a simple description of defects of all codimensions in Kitaev's quantum double model.
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APA:
Faria Martins, J., & Meusburger, C. (2026). A geometrical description of untwisted 3d Dijkgraaf-Witten TQFT with defects. Advances in Mathematics, 494. https://doi.org/10.1016/j.aim.2026.110923
MLA:
Faria Martins, João, and Cathérine Meusburger. "A geometrical description of untwisted 3d Dijkgraaf-Witten TQFT with defects." Advances in Mathematics 494 (2026).
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