Extended 3-dimensional bordism as the theory of modular objects

Bruce Bartlett; Christopher L. Douglas; Christopher J. Schommer-Pries; Jamie Vicary

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arXiv · 1411.0945

Extended 3-dimensional bordism as the theory of modular objects

Bruce Bartlett·Christopher L. Douglas·Christopher J. Schommer-Pries·Jamie Vicary

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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.

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BibTeX RIS

Bruce Bartlett, Christopher L. Douglas, Christopher J. Schommer-Pries, Jamie Vicary. 2014-11-04. Extended 3-dimensional bordism as the theory of modular objects. https://arxiv.org/abs/1411.0945

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