Extended 3-dimensional bordism as the theory of modular objects

2014/11/04 by Bruce Bartlett, Christopher L. Douglas, Bartlett, Bruce +5 · 3 citations
Mathematics · #18D05 #57M25 #57N10 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1411.0945

openalex publication_date 2014/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A modular object in a symmetric monoidal bicategory is a Frobenius algebra object whose product and coproduct are biadjoint, equipped with a braided structure and a compatible twist, satisfying rigidity, ribbon, pivotality, and modularity conditions. We prove that the oriented 3-dimensional bordism bicategory of 1-, 2-, and 3-manifolds is the free symmetric monoidal bicategory on a single anomaly-free modular object.

Citations

• Classical and quantum conformal field theory

Cited by

• Finite semisimple module 2-categories
• Morita Bicategories of Algebras and Duality Involutions
• Modular categories as representations of the 3-dimensional bordism 2-category

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