Hyperbolic three-manifolds that embed geodesically

Bruno Martelli

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arXiv · 1510.06325

Hyperbolic three-manifolds that embed geodesically

Bruno Martelli

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Abstract

We prove that every complete finite-volume hyperbolic 3-manifold $M$ that is tessellated into (embedded) right-angled regular polyhedra (dodecahedra or ideal octahedra) embeds geodesically in a complete finite-volume connected orientable hyperbolic 4-manifold $W$, which is also tessellated into right-angled regular polytopes (120-cells and ideal 24-cells). If $M$ is connected, then Vol($W$) < $2^{49}$Vol($M$). This applies for instance to the Borromean link complement. As a consequence, the Borromean link complement bounds geometrically a hyperbolic 4-manifold.

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Bruno Martelli. 2015-10-21. Hyperbolic three-manifolds that embed geodesically. https://arxiv.org/abs/1510.06325

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