A signed version of Putnam's homology theory: Lefschetz and zeta functions
Robin J. Deeley
TL;DR
This paper introduces a signed version of Putnam homology for Smale spaces, explores its properties, and establishes a Lefschetz theorem, also comparing zeta functions linked to Axiom A diffeomorphisms.
Contribution
It presents a novel signed homology theory for Smale spaces, extending Putnam's framework and connecting it with Lefschetz and zeta functions.
Findings
Definition and basic properties of the signed homology theory
Lefschetz theorem for the signed homology
Comparison of zeta functions for Axiom A diffeomorphisms
Abstract
A signed version of Putnam homology for Smale spaces is introduced. Its definition, basic properties and associated Lefschetz theorem are outlined. In particular, zeta functions associated to an Axiom A diffeomorphism are compared.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory · Topological and Geometric Data Analysis