Hyperbolic manifolds and finite groups
Alexander Lubotzky, The Hebrew University, Israel
Jueves 28 de enero de 2010 a las 11:30 en la sala 520 del módulo 17 de Ciencias, UAM
Resumen: The isometry group of a closed hyperbolic n-manifold is finite. We prove that for every n>1 and every finite group G there is an n-dimensional closed hyperbolic manifold whose isometry group is G. This resolves a long standing problem whose low dimensional cases n=2 and n=3 were proved by Greenberg ('74) and Kojima ('88) resp. The proof is nonconstructive; it uses a 'probabilistic method', i.e. counting results from the theory of 'subgroup growth'.
Joint work with M. Belolipetsky. The talk won't assume any prior knowledge on the subject.