arXiv:0801.3294 Abstract | arXiv Analytics

arXiv:0801.3294 [math.DS]Abstract References Reviews Resources

A homology theory for Smale spaces: a summary

Published 2008-01-22, updated 2008-11-20Version 2

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.

Comments: Research summary; complete version in preparation. The new version gives a substantially simplified and more natural definition

Categories: math.DS

Subjects: 37C70, 37D20, 37B10

Keywords: smale spaces, homology theory, lefschetz formula relating trace data, special case, finite type

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