6 research outputs found
Stein structures: existence and flexibility
This survey on the topology of Stein manifolds is an extract from our recent
joint book. It is compiled from two short lecture series given by the first
author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred
Renyi Institute of Mathematics, Budapest.Comment: 29 pages, 11 figure
A lattice in more than two Kac--Moody groups is arithmetic
Let be an irreducible lattice in a product of n infinite irreducible
complete Kac-Moody groups of simply laced type over finite fields. We show that
if n is at least 3, then each Kac-Moody groups is in fact a simple algebraic
group over a local field and is an arithmetic lattice. This relies on
the following alternative which is satisfied by any irreducible lattice
provided n is at least 2: either is an S-arithmetic (hence linear)
group, or it is not residually finite. In that case, it is even virtually
simple when the ground field is large enough.
More general CAT(0) groups are also considered throughout.Comment: Subsection 2.B was modified and an example was added ther