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By Alexander Kolpakov and Bruno Martelli


Abstract. We introduce an 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 V ln V volume � V grows like C for any fixed k. As a corollary, we deduce that the 3-torus bounds geometrically a hyperbolic manifold. hal-00837649, version 2- 18 Jul 201

Year: 2013
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