A note on TQFTs for orientable 2-dimensional cobordisms

Fuente: arXiv
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Autori principali: Goertz, Leon J., Wedrich, Paul
Natura: Preprint
Pubblicazione: 2025
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author Goertz, Leon J.
Wedrich, Paul
author_facet Goertz, Leon J.
Wedrich, Paul
contents Topological quantum field theories (TQFTs) are symmetric monoidal functors out of cobordism categories. In dimension two, oriented TQFTs are famously classified by commutative Frobenius algebras. In the unoriented setting, the classification requires additional data: an involution and a value assigned to the Möbius strip. In this work, we describe an intermediate framework that classifies 2-dimensional TQFTs for orientable cobordisms, in an appropriate sense. Our motivation arises from skein-theoretic models of surfaces embedded in 3-manifolds and Khovanov homology, where surfaces are often treated as unoriented, even though the associated 2-dimensional TQFTs themselves need not be fully unoriented.
format Preprint
id arxiv_https___arxiv_org_abs_2511_19373
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A note on TQFTs for orientable 2-dimensional cobordisms
Goertz, Leon J.
Wedrich, Paul
Quantum Algebra
Geometric Topology
Topological quantum field theories (TQFTs) are symmetric monoidal functors out of cobordism categories. In dimension two, oriented TQFTs are famously classified by commutative Frobenius algebras. In the unoriented setting, the classification requires additional data: an involution and a value assigned to the Möbius strip. In this work, we describe an intermediate framework that classifies 2-dimensional TQFTs for orientable cobordisms, in an appropriate sense. Our motivation arises from skein-theoretic models of surfaces embedded in 3-manifolds and Khovanov homology, where surfaces are often treated as unoriented, even though the associated 2-dimensional TQFTs themselves need not be fully unoriented.
title A note on TQFTs for orientable 2-dimensional cobordisms
topic Quantum Algebra
Geometric Topology
url https://arxiv.org/abs/2511.19373