Extended 3-dimensional bordism as the theory of modular objects
Geometric Topology
2014-11-05 v1 Algebraic Topology
Category Theory
Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1411.0945,
title = {Extended 3-dimensional bordism as the theory of modular objects},
author = {Bruce Bartlett and Christopher L. Douglas and Christopher J. Schommer-Pries and Jamie Vicary},
journal= {arXiv preprint arXiv:1411.0945},
year = {2014}
}
Comments
64 pages