Unravelling the Dodecahedral Spaces
Geometric Topology
2018-10-24 v2
Abstract
The hyperbolic dodecahedral space of Weber and Seifert has a natural non-positively curved cubulation obtained by subdividing the dodecahedron into cubes. We show that the hyperbolic dodecahedral space has a 6-sheeted irregular cover with the property that the canonical hypersurfaces made up of the mid-cubes give a very short hierarchy. Moreover, we describe a 60-sheeted cover in which the associated cubulation is special. We also describe the natural cubulation and covers of the spherical dodecahedral space (aka Poincar\'e homology sphere).
Keywords
Cite
@article{arxiv.1702.08080,
title = {Unravelling the Dodecahedral Spaces},
author = {Jonathan Spreer and Stephan Tillmann},
journal= {arXiv preprint arXiv:1702.08080},
year = {2018}
}
Comments
15 pages + 6 pages appendix, 7 figures, 4 tables