Abstract.
It will be shown that every minimal Cantor set can be obtained as a projective limit of directed graphs. This allows to study minimal Cantor sets by algebraic topological means. In particular, homology, homotopy and cohomology are related to the dynamics of minimal Cantor sets. These techniques allow to explicitly illustrate the variety of dynamical behavior possible in minimal Cantor sets.
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Communicated by Jean Bellissard
submitted 20/07/05, accepted 18/10/05
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Gambaudo, JM., Martens, M. Algebraic Topology for Minimal Cantor Sets. Ann. Henri Poincaré 7, 423–446 (2006). https://doi.org/10.1007/s00023-005-0255-3
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DOI: https://doi.org/10.1007/s00023-005-0255-3