Limits of (certain) CAT(0) groups, II: The Hopf property and the shortening argument

Details Limits of (certain) CAT(0) groups, II: The Hopf property and the shortening argument Limits of (certain) CAT(0) groups, II: The Hopf property and the shortening argument

2004-08-05

arxiv.org/abs/math/0408080v1

Mathematics

Group Theory

38 pages

Scientific paper

This is the second in a series of papers about torsion-free groups which act properly and cocompactly on a CAT(0) metric space with isolated flats and relatively thin triangles. Our approach is to adapt the methods of Sela and others for word-hyperbolic groups to this context of non-positive curvature. The main result in this paper is that (under certain technical hypotheses) such a group as above is Hopfian. This (mostly) answers a question of Sela.

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