Property (FA) and lattices in SU(2,1)
Geometric Topology
2007-10-18 v2 Group Theory
Abstract
In this paper we consider Property (FA) for lattices in SU(2,1). First, we prove that SU(2,1;O_3) has Property (FA). We then prove that the arithmetic lattices in SU(2,1) of second type arising from congruence subgroups studied by Rapoport--Zink and Rogawski cannot split as a nontrivial free product with amalgamation; one such example is Mumford's fake projective plane. In fact, we prove that the fundamental group of any fake projective plane has Property (FA).
Cite
@article{arxiv.math/0512180,
title = {Property (FA) and lattices in SU(2,1)},
author = {Matthew Stover},
journal= {arXiv preprint arXiv:math/0512180},
year = {2007}
}
Comments
To appear in IJAC