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Combinatorial and Geometric Group Theory
May 5-10, 2006
Vanderbilt University
Nashville, TN, USA

Organizers
Goulnara Arzhantseva, Mike Mihalik, Denis Osin, Mark Sapir, Efim Zelmanov

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Nagata-Assouad dimension via Lipschitz extensions
by
Jose Higes
Universidad Complutense de Madrid, Spain.
Coauthors: Nikolay Brodskiy (University of Tennessee) Jerzy Dydak (University of Tennessee) Atish Mitra (University of Tennessee)

Abstract

In the first part we show how to relate several dimension theories (asymptotic dimension with Higson property, asymptotic dimension of Gromov, and capacity dimension of Buyalo) to Nagata-Assouad dimension. This is done by applying two functors on the Lipschitz category of metric spaces: microscopic and macroscopic. In the second part we identify (among spaces of finite Nagata-Assouad dimension) spaces of Nagata-Assouad dimension at most n as those for which the n-sphere Sn is a Lipschitz extensor. Large scale and small scale analogs of that result are given.

Date received: March 1, 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 # caqu-67.