Cocompact lattices in locally compact Kac-Moody groups

Anne Thomas (University of Glasgow)

Wednesday 25th September, 2013 16:00-17:00 Maths 204


A locally compact group G is a group with compatible algebraic,
topological and measure-theoretic structures.  A connected example is
G = SL(n,R), and a totally disconnected example is G = SL(n,K), where
K is the field of Laurent polynomials over the finite field F_q.  A
cocompact lattice in a locally compact group G is a discrete subgroup
\Gamma so that the coset space G / \Gamma is compact.  We construct
the first examples of cocompact lattices in many locally compact
Kac-Moody groups G.  These groups G are totally disconnected and in
general non-linear, but they act "nicely" on an associated cell 
complex called a building.  We use this action to construct our
examples, which include lattices with surface subgroups and lattices
which are free groups.  This is joint work with Inna Capdeboscq.

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