2021/07/03 by Hou, Bingzhe, Igusa, Kiyoshi, Liu, Zihao
#Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2107.01313
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.