The amazing world of simplicial complexes

2018/04/23 by Oliver Knill, Knill, Oliver · 2 citations
Computer Science · Mathematics · #05Exx #15A36 #51-xx #55-xx #68-xx #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #History and Overview (math.HO) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.CO #math.HO #msc:05Exx #msc:15A36 #msc:51-xx #msc:55-xx #msc:68-xx

paper · pdf · doi:10.48550/arxiv.1804.08211

Notes made for preparing for the AMS special session "Discretization in Geometry" in Boston on April 22, 2018

arxiv created 2018/04/23 · openalex publication_date 2018/04/23 · arxiv updated 2018/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Defined by a single axiom, finite abstract simplicial complexes belong to the simplest constructs of mathematics. We look at a a few theorems.

Citations

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Cited by

• A Reeb sphere theorem in graph theory
• The average simplex cardinality of a finite abstract simplicial complex

Related

• Foundations of Simplicial Complexes:From Geometric Independence to Realizations
• Simplicial Structure on Complexes
• Pure Simplicial and Clique Complexes with a Fixed Number of Facets
• Fundamental Groups of Simplicial Complexes
• An elementary illustrated introduction to simplicial sets