Property (FA) and Lattices in su(2, 1)

In this paper we consider Property (FA) for lattices in SU(2, 1). First, we prove that SU(2, 1; O3) 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).

• Type: Journal
• Year: 2007
• Where: IJAC
• Authors: Matthew Stover
• Keywords: Congruence Subgroups, Fake Projective Plane, IJAC 2007, Nontrivial Free Product