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arXiv 0801.32942008-01math.DS

Smale空间的同调论综述

A homology theory for Smale spaces: a summary

Ian F. Putnam

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

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摘要：

我们考虑Smale空间，一类特殊的双曲拓扑动力系统，其中包括Smale公理A系统的基本集合。我们给出了这类系统的一个同调论，它是基于有限型移位的特殊情况下的维数群。该理论提供了一个Lefschetz公式，该公式将跟踪数据与系统的周期点的数量相关联。

英文摘要：

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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