Modular categories as representations of the 3-dimensional bordism 2-category
Bruce Bartlett, Christopher L. Douglas, Christopher J. Schommer-Pries, and Jamie Vicary
TL;DR
This paper establishes a correspondence between certain 3D topological quantum field theories and modular tensor categories with specific dimension properties, deepening the understanding of their mathematical structure.
Contribution
It introduces a canonical bijection linking once-extended anomalous 3D TQFTs to modular tensor categories with a square root of global dimension.
Findings
Bijection between 3D TQFTs and modular tensor categories.
Characterization of TQFTs via modular categories with dimension square roots.
Enhanced understanding of the algebraic structures underlying 3D topological phases.
Abstract
We show that once-extended anomalous 3-dimensional topological quantum field theories valued in the 2-category of k-linear categories are in canonical bijection with modular tensor categories equipped with a square root of the global dimension in each factor.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra