2025/11/24 by Goertz, Leon J., Wedrich, Paul
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2511.19373
openalex publication_date 2025/11/24 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28
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.