2017/12/22 by Patrick Erik Bradley, Bradley, Patrick Erik
Computer Science · Mathematics · #55U15 #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1712.08549
openalex publication_date 2017/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new method is given for computing generators of the homology groups with integer coefficients for any finite T0-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous injective maps between spaces called immersions. The so-called orb complex which is much smaller than the order complex induces a surjective map of its homology to the simplicial homology of the space. An analysis of the kernel of this map allows to define an effective algorithm for computing the homology groups, whose time complexity is polynomial in the size of the space.