Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Riemannian_manifold
CW complex |
| gptkbp:b_0 |
number of connected components
|
| gptkbp:b_1 |
number of independent loops
|
| gptkbp:b_2 |
number of independent voids
|
| gptkbp:category |
gptkb:topology
|
| gptkbp:describes |
gptkb:topology
|
| gptkbp:field |
gptkb:topology
|
| gptkbp:firstBettiNumber |
number of independent 1-dimensional cycles
|
| gptkbp:generalizes |
gptkb:Euler_characteristic
|
| https://www.w3.org/2000/01/rdf-schema#label |
Betti numbers
|
| gptkbp:introducedIn |
19th century
|
| gptkbp:isSequence |
b_0, b_1, b_2, ...
|
| gptkbp:measures |
number of independent cycles
|
| gptkbp:namedAfter |
gptkb:Enrico_Betti
|
| gptkbp:notation |
b_n
|
| gptkbp:relatedTo |
homology group
|
| gptkbp:secondBettiNumber |
number of independent 2-dimensional cycles
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:cohomology_theory differential geometry topological data analysis |
| gptkbp:bfsParent |
gptkb:Weil_conjectures
gptkb:Kähler_manifold |
| gptkbp:bfsLayer |
5
|