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Tuesday Seminar on Topology
Seminar information archive ～05/23｜Next seminar｜Future seminars 05/24～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | HABIRO Kazuo, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2013/12/03
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Bruno Martelli (Univ. di Pisa)
Hyperbolic four-manifolds with one cusp (cancelled) (JAPANESE)
Bruno Martelli (Univ. di Pisa)
Hyperbolic four-manifolds with one cusp (cancelled) (JAPANESE)
[ Abstract ]
(joint work with A. Kolpakov)
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.
(joint work with A. Kolpakov)
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.
