Property (FA) and lattices in SU(2,1)

Details Property (FA) and lattices in SU(2,1) Property (FA) and lattices in SU(2,1)

2005-12-08

arxiv.org/abs/math/0512180v2

Mathematics

Geometric Topology

To appear in IJAC

Scientific paper

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).

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