Algebraic topology for minimal cantor sets

Jean Marc Gambaudo; Marco Martens

doi:10.1007/s00023-005-0255-3

Algebraic topology for minimal cantor sets

Jean Marc Gambaudo
, Marco Martens

Mathematics

Stony Brook University

Universidad de Chile

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

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.

Original language	English
Pages (from-to)	423-446
Number of pages	24
Journal	Annales Henri Poincare
Volume	7
Issue number	3
DOIs	https://doi.org/10.1007/s00023-005-0255-3
State	Published - May 2006

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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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AB - 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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JO - Annales Henri Poincare

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Algebraic topology for minimal cantor sets

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