Right-angled Coxeter polytopes, hyperbolic six-manifolds and a problem of Siegel

Brent Everitt; John Ratcliffe; Steven Tschantz

doi:10.1007/s00208-011-0744-2

Right-angled Coxeter polytopes, hyperbolic six-manifolds and a problem of Siegel

Brent Everitt, John Ratcliffe, Steven Tschantz

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

By gluing together the sides of eight copies of an all-right angled hyperbolic 6-dimensional polytope, two orientable hyperbolic 6-manifolds with Euler characteristic -1 are constructed. They are the first known examples of orientable hyperbolic 6-manifolds having the smallest possible volume.

Original language	English
Pages (from-to)	871-905
Number of pages	32
Journal	Mathematische Annalen
Volume	354
Issue number	3
Early online date	16 Nov 2011
DOIs	https://doi.org/10.1007/s00208-011-0744-2
Publication status	Published - Nov 2012

Keywords

Algebra

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10.1007/s00208-011-0744-2

http://link.springer.com/article/10.1007%2Fs00208-011-0744-2

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title = "Right-angled Coxeter polytopes, hyperbolic six-manifolds and a problem of Siegel",

abstract = "By gluing together the sides of eight copies of an all-right angled hyperbolic 6-dimensional polytope, two orientable hyperbolic 6-manifolds with Euler characteristic -1 are constructed. They are the first known examples of orientable hyperbolic 6-manifolds having the smallest possible volume.",

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AB - By gluing together the sides of eight copies of an all-right angled hyperbolic 6-dimensional polytope, two orientable hyperbolic 6-manifolds with Euler characteristic -1 are constructed. They are the first known examples of orientable hyperbolic 6-manifolds having the smallest possible volume.

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Right-angled Coxeter polytopes, hyperbolic six-manifolds and a problem of Siegel

Abstract

Keywords

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