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arXiv · 2107.01313

Scaled Homology and Topological Entropy

Bingzhe Hou·Kiyoshi Igusa·Zihao Liu
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Abstract

In this paper, we build up a scaled homology theory, $lc$-homology, for metric spaces such that every metric space can be visually regarded as "locally contractible" with this newly-built homology. We check that $lc$-homology satisfies all Eilenberg-Steenrod axioms except exactness axiom whereas its corresponding $lc$-cohomology satisfies all axioms for cohomology. This homology can relax the smooth manifold restrictions on the compact metric space such that the entropy conjecture will hold for the first $lc$-homology group.

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Bingzhe Hou, Kiyoshi Igusa, Zihao Liu. 2021-07-03. Scaled Homology and Topological Entropy. https://arxiv.org/abs/2107.01313

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