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G^3 = Geometric Group Theory on the Gulf Coast
January 9-12, 2007

New Orleans, LA, USA

Organizers
Stephen Brick, Craig Jensen, Igor Mineyev.

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Asymptotic Assouad-Nagata Dimension via Compactifications
by
Justin Smith
University of Florida
Coauthors: Alexander Dranishnikov (University of Florida)

Assouad introduced a metric invariant called Nagata dimension to simplify a construction of Nagata. Later this dimension was applied to some embedding theorems in hyperbolic geometry and it acquired the name Assouad-Nagata dimension. We show that the Assouad-Nagata dimension of a finitely generated group equals the covering dimension of the Higson corona for a certain coarse structure. We also give conditions under which the dimension of the asymptotic cone over a metric space X does not exceed the asymptotic Assouad-Nagata dimension of X.

Date received: December 13, 2006

Copyright © 2006 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # catr-09.