Counting Hyperbolic Manifolds

By M. Burger, Tsachik Gelander, Alexander Lubotzky, Shahar Mozes. 2002

71 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ca8dc7fbb76114ff98d34aeb93361b452a2513d9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Tsachik Gelander
2. Mikhail G. Katz
3. Alexander Lubotzky

In Geometry and Topology

1. Mikhail V. Belolipetsky
2. Mikhail G. Katz
3. Tsachik Gelander
4. S. Sabourau
5. Alexander Lubotzky
6. Emmanuel Breuillard
7. Richard Aoun
8. William P. Thurston

In Mathematical Physics

1. Mikhail V. Belolipetsky
2. Mikhail G. Katz
3. Tsachik Gelander
4. S. Sabourau
5. Alexander Lubotzky
6. David Sherry
7. William P. Thurston
8. Nathan M. Dunfield

Citations in the corpus

• Homotopy type and volume of locally symmetric manifolds (2001, methodology): “ee lattices (uniform and nonuniform) for any rank-1 group, with the two familiar exceptional PSL2(R) 3 and PSL2(C) for which Wang’s theorem is not true. This generalizes the (upper bound) result from [6]. In section 6 we show how our method gives an estimate for the growth function of irreducible la”
• Finite groups and hyperbolic manifolds (2004, background): “It may be of interest to give some bounds on f(n,G). We mention by passing that for n≥ 4 and a given r>0, there are only finitely many n-dimensional hyperbolic manifolds of volume at most r[Wa]. In [BGLM], it is shown that the growth rate of the number of manifolds is like exp(c(n)rlogr). One may ”
• Entropy of systolically extremal surfaces and asymptotic bounds (2004, background): “Related arguments have been exploited in [ BM02 , Ge04].”