Unravelling the Dodecahedral Spaces

Jonathan Spreer; Stephan Tillmann

doi:10.1007/978-3-319-72299-3_17

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arXiv · 1702.08080

Unravelling the Dodecahedral Spaces

Jonathan Spreer·Stephan Tillmann

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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 Poincaré homology sphere).

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BibTeX RIS

Jonathan Spreer, Stephan Tillmann. 2017-07-02. Unravelling the Dodecahedral Spaces. https://doi.org/10.1007/978-3-319-72299-3_17

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