EZ-structures and topological applications

2004/05/13 by F. T. Farrell, J. -F. Lafont
Mathematics · #math.GT #math.KT

paper · pdf

published as Comment. Math. Helv., 80 (2005), pgs. 103-121. · 21 pages, final version will appear in Comment. Math. Helv

arxiv created 2004/05/13 · arxiv updated 2009/12/01

Abstract

We introduce the notion of an EZ-structure on a group. Delta-hyperbolic groups and CAT(0)-groups have EZ-structures. We show torsion-free groups having an EZ-structure automatically have an action by homeomorphisms on a closed (high-dimensional) ball, which is well-behaved away from a "bad limit set" in the boundary of the ball. We show that groups having such an action satisfy the Novikov conjecture. For torsion-free delta-hyperbolic groups G, we also give a lower bound for the homotopy groups π_n(P(BG)), where P is the stable topological pseudo-isotopy functor.

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