 

Fred Shultz
Dimension groups for interval maps


Published: 
October 29, 2005

Keywords: 
dimension group, interval map, piecewise monotonic, unimodal map, tent map, βshift, interval exchange map, C*algebra 
Subject: 
Primary 37E05, 46L80 


Abstract
With each piecewise monotonic map τ of the unit interval,
a dimension triple is associated. The dimension triple, viewed as a
Z[t,t^{1}] module, is finitely generated, and generators are identified.
Dimension groups are computed for Markov maps, unimodal maps, multimodal maps,
and interval exchange maps.
It is shown that the dimension group defined here is isomorphic to K_{0}(A),
where A is a C*algebra (an "AIalgebra") defined in dynamical terms.


Acknowledgements
The author gratefully acknowledges partial support for this work by a Brachman Hoffman Fellowship from Wellesley College.


Author information
Wellesley College,Wellesley, Massachusetts 02481
fshultz@wellesley.edu

