New York Journal of Mathematics
Volume 11 (2005) 477-517


Fred Shultz

Dimension groups for interval maps

Published: October 29, 2005
Keywords: dimension group, interval map, piecewise monotonic, unimodal map, tent map, β-shift, interval exchange map, C*-algebra
Subject: Primary 37E05, 46L80


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 K0(A), where A is a C*-algebra (an "AI-algebra") defined in dynamical terms.


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

Author information

Wellesley College,Wellesley, Massachusetts 02481