2023/11/13 by Sara Faridi, Thiago Holleben, Faridi, Sara +1
Computer Science · Mathematics · #05E40 #05E45 #13F55 #55P15 #55U10 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2311.07727
openalex publication_date 2023/11/13 · openalex created_date 2023/11/16 · openalex updated_date 2026/07/28
In this paper we define spherical complexes as simplicial complexes with the property that every subcomplex obtained by a sequence of links and deletions either has trivial homology, or has the homology of a sphere. Examples of such complexes are independence complexes of ternary graphs and independence complexes of simplicial forests. We give criteria for when a spherical complex is acyclic, and describe the dimension of the sphere when it is not. We then apply our results to compute the Leray number of these complexes, and define combinatorial invariants for them which are counterparts to algebraic invariants of their Stanley-Reisner rings.