Homology for one-dimensional solenoids
DOI:
https://doi.org/10.7146/math.scand.a-26265Abstract
Smale spaces are a particular class of hyperbolic topological dynamical systems, defined by David Ruelle. The definition was introduced to give an axiomatic description of the dynamical properties of Smale's Axiom A systems when restricted to a basic set. They include Anosov diffeomeorphisms, shifts of finite type and various solenoids constructed by R. F. Williams. The second author constructed a homology theory for Smale spaces which is based on (and extends) Krieger's dimension group invariant for shifts of finite type. In this paper, we compute this homology for the one-dimensional generalized solenoids of R. F. Williams.
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