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Hyperbolic three-manifolds that embed geodesically
- Publication Year :
- 2015
- Publisher :
- arXiv, 2015.
-
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.<br />11 pages, 6 figures. Mistake corrected: the decomposition needs to be "nice" in order to avoid self-adjacent (and hence uncolourable) facets
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....4c8080894f7e67d2aeebb90a97e62832
- Full Text :
- https://doi.org/10.48550/arxiv.1510.06325