Experimental Mathematics

The volume spectrum of hyperbolic 4-manifolds

John G. Ratcliffe and Steven T. Tschantz

Abstract

We construct complete, open, hyperbolic 4-manifolds of smallest volume by gluing together the sides of a regular ideal 24-cell in hyperbolic 4-space. We also show that the volume spectrum of hyperbolic 4-manifolds is the set of all positive integral multiples of $4\pi^2/3$.

Article information

Source
Experiment. Math., Volume 9, Issue 1 (2000), 101-125.

Dates
First available in Project Euclid: 5 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1046889595

Mathematical Reviews number (MathSciNet)
MR1758804

Zentralblatt MATH identifier
0963.57012

Subjects
Primary: 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx]
Secondary: 57M50: Geometric structures on low-dimensional manifolds

Keywords
Hyperbolic manifolds 4-manifolds volume 24-cell

Citation

Ratcliffe, John G.; Tschantz, Steven T. The volume spectrum of hyperbolic 4-manifolds. Experiment. Math. 9 (2000), no. 1, 101--125. https://projecteuclid.org/euclid.em/1046889595


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