A homology theory for Smale spaces: a summary
Dynamical Systems
2008-11-20 v2
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.
Cite
@article{arxiv.0801.3294,
title = {A homology theory for Smale spaces: a summary},
author = {Ian F. Putnam},
journal= {arXiv preprint arXiv:0801.3294},
year = {2008}
}
Comments
Research summary; complete version in preparation. The new version gives a substantially simplified and more natural definition