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arxiv: 1411.0945 · v1 · pith:QVDOBJFZnew · submitted 2014-11-04 · 🧮 math.GT · math.AT· math.CT· math.QA

Extended 3-dimensional bordism as the theory of modular objects

Bruce Bartlett , Christopher L. Douglas , Christopher J. Schommer-Pries , Jamie Vicary This is my paper
classification 🧮 math.GT math.ATmath.CTmath.QA
keywords bicategorymodularobjectbordismdimensionalmonoidalsymmetricalgebra
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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.

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