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Some hyperbolic 4-manifolds with low volume and number of cusps

Abstract

We construct here two new examples of non-orientable, non-compact, hyperbolic 4-manifolds. The first has minimal volume vm=4Ï€2/3v_m = 4{\pi}^2/3 and two cusps. This example has the lowest number of cusps among known minimal volume hyperbolic 4-manifolds. The second has volume 2â‹…vm2\cdot v_m and one cusp. It has lowest volume among known one-cusped hyperbolic 4-manifolds.Comment: 12 pages, 11 figure

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