Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
gptkb:Network_science
Mesh generation Persistent homology Topological data analysis |
| gptkbp:canBe |
Infinite
Geometric Abstract Finite |
| gptkbp:component |
gptkb:Simplex
|
| gptkbp:definedIn |
A set of simplices that satisfies certain intersection properties
|
| gptkbp:example |
Boundary of a tetrahedron
Nerve of a cover Triangulation of a surface |
| gptkbp:field |
gptkb:Algebraic_topology
gptkb:Topology Combinatorics |
| gptkbp:generalizes |
Graphs
Polyhedra |
| gptkbp:hasInvariant |
gptkb:Euler_characteristic
gptkb:Cohomology Homology |
| https://www.w3.org/2000/01/rdf-schema#label |
Simplicial Complexes
|
| gptkbp:property |
Dimension
Finite or infinite Closed under taking faces Pure or non-pure |
| gptkbp:relatedConcept |
gptkb:Cell_complex
gptkb:Delta_complex gptkb:Simplicial_set Polyhedral complex |
| gptkbp:relatedTo |
CW complexes
Abstract simplicial complex Geometric realization |
| gptkbp:structure |
gptkb:Homology_groups
gptkb:Chain_complex Cohomology groups Face poset |
| gptkbp:studiedBy |
gptkb:Henri_Poincaré
gptkb:J._H._C._Whitehead |
| gptkbp:used_in |
Homology theory
Combinatorial topology Computational topology |
| gptkbp:usedFor |
Approximating topological spaces
Computing Betti numbers Discrete Morse theory Modeling higher-order interactions Studying homotopy type |
| gptkbp:bfsParent |
gptkb:Singular_Homology_Theory
|
| gptkbp:bfsLayer |
7
|