|
gptkbp:instanceOf
|
gptkb:mathematical_concept
gptkb:topology
|
|
gptkbp:can_be_triangulated
|
yes
|
|
gptkbp:canBe
|
compact
non-orientable
orientable
non-compact
|
|
gptkbp:category
|
PL category
|
|
gptkbp:contrastsWith
|
gptkb:topology
gptkb:Riemannian_manifold
|
|
gptkbp:definedIn
|
a topological manifold with a piecewise-linear structure
|
|
gptkbp:dimensions
|
n (for any integer n ≥ 1)
|
|
gptkbp:field
|
gptkb:topology
differential geometry
|
|
gptkbp:hasApplication
|
knot theory
low-dimensional topology
|
|
gptkbp:hasProperty
|
locally homeomorphic to Euclidean space
transition maps are piecewise-linear
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
PL manifold
|
|
gptkbp:importantFor
|
surgery theory
triangulation theory
|
|
gptkbp:introduced
|
gptkb:John_Milnor
gptkb:John_Stallings
|
|
gptkbp:relatedTo
|
gptkb:topology
gptkb:Riemannian_manifold
|
|
gptkbp:standsFor
|
piecewise-linear manifold
|
|
gptkbp:structure
|
piecewise-linear atlas
|
|
gptkbp:studiedBy
|
geometric topology
|
|
gptkbp:used_in
|
classification of manifolds
combinatorial topology
|
|
gptkbp:bfsParent
|
gptkb:The_smooth_4-dimensional_triangulation_conjecture
|
|
gptkbp:bfsLayer
|
7
|