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arXiv · 0801.3294

A homology theory for Smale spaces: a summary

Ian F. Putnam
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Abstract

We consider Smale spaces, a particular class of hyperbolic topological dynamical systems, which include the basic sets for Smale's Axiom A systems. We present a homology theory for such systems which is based on the dimension group in the special case of shifts of finite type. This theory provides a Lefschetz formula relating trace data with the number of periodic points of the system.

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Ian F. Putnam. 2008-11-20. A homology theory for Smale spaces: a summary. https://arxiv.org/abs/0801.3294

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