We introduce a simple algorithm which transforms every four-dimensional cubulation into a cusped finite-volume hyperbolic four-manifold. Combinatorially distinct cubulations give rise to topologically distinct manifolds. Using this algorithm we construct the first examples of finite-volume hyperbolic four-manifolds with one cusp. More generally, we show that the number of k-cusped hyperbolic four-manifolds with volume smaller than V grows like C^{V log V} for any fixed k. As a corollary, we deduce that the 3-torus bounds geometrically a hyperbolic manifold.

Hyperbolic four-manifolds with one cusp

MARTELLI, BRUNO
2013

Abstract

We introduce a simple algorithm which transforms every four-dimensional cubulation into a cusped finite-volume hyperbolic four-manifold. Combinatorially distinct cubulations give rise to topologically distinct manifolds. Using this algorithm we construct the first examples of finite-volume hyperbolic four-manifolds with one cusp. More generally, we show that the number of k-cusped hyperbolic four-manifolds with volume smaller than V grows like C^{V log V} for any fixed k. As a corollary, we deduce that the 3-torus bounds geometrically a hyperbolic manifold.
Alexander, Kolpakov; Martelli, Bruno
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/236740
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