Dimension groups for interval maps

Details Dimension groups for interval maps Dimension groups for interval maps

2004-05-24

arxiv.org/abs/math/0405466v2

Mathematics

Dynamical Systems

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

Scientific paper

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.

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