Dimension groups for interval maps

Abstract

With each piecewise monotonic map 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 "AI-algebra") defined in dynamical terms.

40 pages, 2 postscript (eps) figures, LateX. Editorial corrections. Has been accepted for publication in the New York Journal of Mathematics