2011/09/09 by Volker Thürey, Volker W. Thürey, Thürey, Volker W.
Computer Science · Mathematics · #51M04 #55N20 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.GT #msc:51M04 #msc:55N20
paper · pdf · doi:10.48550/arxiv.1109.2161
33 pages, 17 figures and diagrams
arxiv created 2011/09/09 · openalex publication_date 2011/09/09 · arxiv updated 2011/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize the very well known boundary operator of the ordinary singular homology theory, defined in many books about algebraic topology. We describe a variant of this ordinary simplicial boundary operator where the usual boundary (n-1)-simplices of each n-simplex are replaced by combinations of internal (n-1)- simplices parallel to the faces. This construction may lead to an infinite class of extraordinary non-isomorphic homology theories. We show further some interesting constructions on the standard simplex.