Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
π₁
|
| gptkbp:category |
gptkb:topology
group theory |
| gptkbp:dependsOn |
base point
|
| gptkbp:describes |
loops up to homotopy
|
| gptkbp:example |
π₁(S¹) ≅ ℤ
π₁(Torus) ≅ ℤ × ℤ π₁(ℝⁿ) is trivial for n ≥ 2 |
| gptkbp:field |
gptkb:topology
|
| gptkbp:hasInvariant |
gptkb:topology
|
| https://www.w3.org/2000/01/rdf-schema#label |
fundamental group
|
| gptkbp:introduced |
gptkb:Henri_Poincaré
|
| gptkbp:isFunctor |
category of topological spaces to category of groups
|
| gptkbp:isNonAbelian |
if and only if the space is locally path-connected and simply connected
|
| gptkbp:isTrivialFor |
simply connected spaces
|
| gptkbp:notation |
π₁(X, x₀)
|
| gptkbp:relatedTo |
homology
covering space theory higher homotopy groups |
| gptkbp:usedIn |
classification of covering spaces
study of path-connectedness |
| gptkbp:bfsParent |
gptkb:topology
gptkb:knot gptkb:Topology gptkb:Group_theory gptkb:Riemannian_manifold gptkb:Lie_group gptkb:Lie_groups |
| gptkbp:bfsLayer |
5
|