A homology theory for Smale spaces: a summary
Abstract
Description
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.
Research summary; complete version in preparation. The new version gives a substantially simplified and more natural definition
Research summary; complete version in preparation. The new version gives a substantially simplified and more natural definition