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arXiv · 1204.6161

Trees of nuclei and bounds on the number of triangulations of the 3-ball

Pierre Collet·Jean-Pierre Eckmann·Maher Younan
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Abstract

Based on the work of Durhuus-J{ó}nsson and Benedetti-Ziegler, we revisit the question of the number of triangulations of the 3-ball. We introduce a notion of nucleus (a triangulation of the 3-ball without internal nodes, and with each internal face having at most 1 external edge). We show that every triangulation can be built from trees of nuclei. This leads to a new reformulation of Gromov's question: We show that if the number of rooted nuclei with $t$ tetrahedra has a bound of the form $C^t$, then the number of rooted triangulations with $t$ tetrahedra is bounded by $C_*^t$.

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Pierre Collet, Jean-Pierre Eckmann, Maher Younan. 2012-04-27. Trees of nuclei and bounds on the number of triangulations of the 3-ball. https://arxiv.org/abs/1204.6161

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