Dimension groups for interval maps

摘要

With each piecewise monotonic map τ of the unit interval,a dimension triple is associated. The dimension triple, viewed as aZ[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.