English

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.

Keywords

Cite

@article{arxiv.2104.02101,
  title  = {A universal state sum},
  author = {Kevin Walker},
  journal= {arXiv preprint arXiv:2104.02101},
  year   = {2021}
}

Comments

v1: no comments

R2 v1 2026-06-24T00:51:57.218Z