A strong Schottky Lemma for nonpositively curved singular spaces

Details A strong Schottky Lemma for nonpositively curved singular spaces A strong Schottky Lemma for nonpositively curved singular spaces

2001-01-09

arxiv.org/abs/math/0101074v1

Mathematics

Group Theory

Scientific paper

In this paper we give a criterion for pairs of isometries of a nonpositively curved metric space to generate a free group. This criterion holds only in singular spaces, for example in Euclidean buildings. The original motivation for our criterion was to prove that the four dimensional Burau representation is faithful. Although we do not settle this question, we do exhibit a related 2-parameter family of faithful representations of the free group F_2.

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