Non-coherence of arithmetic hyperbolic lattices

Details Non-coherence of arithmetic hyperbolic lattices Non-coherence of arithmetic hyperbolic lattices

2010-05-22

arxiv.org/abs/1005.4135v1

Mathematics

Group Theory

26 pages, 3 figures

Scientific paper

We prove, under the assumption of the virtual fibration conjecture for
arithmetic hyperbolic 3-manifolds, that all arithmetic lattices in O(n,1), n>
4, and different from 7, are non-coherent. We also establish noncoherence of
uniform arithmetic lattices of the simplest type in SU(n,1), n> 1, and of
uniform lattices in SU(2,1) which have infinite abelianization.

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