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Bounded rigidity of manifolds and asymptotic dimension growth

Published online by Cambridge University Press:  07 January 2008

Stanley S. Chang ,
Steven Ferry  and
Guoliang Yu
Stanley S. Chang
Affiliation:
[email protected] of Mathematics, Wellesley College, MA 02481, USA
Steven Ferry
Affiliation:
[email protected] of Mathematics, Rutgers University, Piscataway NJ 08854, USA
Guoliang Yu
Affiliation:
[email protected] of Mathematics, Vanderbilt University, Nashville TN 37240, USA
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Abstract

We provide a bounded rigidity result for uniformly contractible manifolds with bounded geometry and sufficiently slow asymptotic dimension growth. This notion of asymptotic growth is a generalization of Gromov's definition of asymptotic dimension. In particular for these manifolds we prove that the bounded assembly map is an isomorphism. Our result is inspired by the coarse Baum-Connes results of Yu and the development of squeezing structures.

Keywords

Bounded rigiditynoncompact manifoldsasymptotic dimension
Type
Research Article
Information
Journal of K-Theory , Volume 1 , Issue 1 , February 2008 , pp. 129 - 144
Copyright
Copyright © ISOPP 2008

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