A universal state sum
Quantum Algebra
2021-04-07 v1 Geometric Topology
Abstract
We define a universal state sum construction which specializes to most previously known state sums (Turaev-Viro, Dijkgraaf-Witten, Crane-Yetter, Douglas-Reutter, Witten-Reshetikhin-Turaev surgery formula, Brown-Arf). The input data for the state sum is an n-category satisfying various conditions, including finiteness, semisimplicity and n-pivotality. From this n-category one constructs an n+1-dimensional TQFT, and applying the TQFT gluing rules to a handle decomposition of an n+1-manifold produces the state sum.
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Cite
@article{arxiv.2104.02101,
title = {A universal state sum},
author = {Kevin Walker},
journal= {arXiv preprint arXiv:2104.02101},
year = {2021}
}
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