Combinatorial description of closed $3$-manifolds via ordered ideal triangulations

Stavros Garoufalidis; Rinat Kashaev; Sakie Suzuki

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arXiv · 2605.29443

Combinatorial description of closed $3$-manifolds via ordered ideal triangulations

Stavros Garoufalidis·Rinat Kashaev·Sakie Suzuki

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Abstract

It is well known that every compact oriented 3-manifold admits an ideal triangulation, and that any two such triangulations with at least two ideal tetrahedra are related by a sequence of Pachner $2$-$3$ moves. Motivated by constructions in quantum topology, we give a combinatorial description of closed $3$-manifolds in terms of ordered ideal triangulations and ordered Pachner $2$-$3$ and $0$-$2$ moves.

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Stavros Garoufalidis, Rinat Kashaev, Sakie Suzuki. 2026-05-28. Combinatorial description of closed $3$-manifolds via ordered ideal triangulations. https://arxiv.org/abs/2605.29443

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