Reconstructing Turaev-Viro Invariants from Four-Fold Simple Branched Covering Presentations

Eri Hatakenaka

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arXiv · 2608.13241

Reconstructing Turaev-Viro Invariants from Four-Fold Simple Branched Covering Presentations

Eri Hatakenaka

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Abstract

We construct a finite state sum from a link diagram labelled by transpositions. The diagram presents a closed 3-manifold as a four-fold simple branched cover, and the state sum equals the SU(2)-type Turaev-Viro invariant of that manifold. For each admissible colouring of the diagram's edges and complementary regions, a global factor is combined with crossing weights obtained by summing over compatible local colourings. We then sum these products over all diagram colourings. The formula is proved by assembling crossing-wise local triangulations and matching the two state sums.

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Eri Hatakenaka. 2026-08-13. Reconstructing Turaev-Viro Invariants from Four-Fold Simple Branched Covering Presentations. https://arxiv.org/abs/2608.13241

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