Seifert fibered spaces

E911225

Seifert fibered spaces are three-dimensional manifolds that can be decomposed into a disjoint union of circles arranged in a highly structured, fibered way over a two-dimensional orbifold.

All labels observed (4)

Label Occurrences
Seifert fibered spaces canonical 2
Haken 3-manifolds 1
Seifert fibration 1

How this entity was disambiguated

Statements (49)

Predicate Object
instanceOf 3-manifold ⓘ
fiber bundle (up to singular fibers) ⓘ
mathematical concept ⓘ
appearsIn Thurston eight geometries ⓘ
Thurston geometrization conjecture ⓘ
baseDimension 2 ⓘ
baseOrbifoldProperty base orbifold may have cone points ⓘ
base orbifold may have reflector curves ⓘ
baseSpace 2-dimensional orbifold ⓘ
classifiedBy Euler number of the fibration ⓘ
Seifert invariants ⓘ
base orbifold ⓘ
multiplicities of singular fibers ⓘ
constructionMethod Dehn filling on a circle bundle over a surface ⓘ
covers circle bundle over a surface (in some cases) ⓘ
dimension 3 ⓘ
fiber S^1 ⓘ
circle ⓘ
field 3-manifold theory ⓘ
geometric topology ⓘ
fundamentalGroupProperty contains infinite cyclic normal subgroup generated by a regular fiber ⓘ
generalizes circle bundles over closed surfaces ⓘ
hasComponent regular fibers ⓘ
singular fibers ⓘ
hasExample 3-sphere with Hopf fibration ⓘ
S^2 × S^1 ⓘ
lens spaces ⓘ
torus bundles over S^1 ⓘ
hasFundamentalGroup group fitting into short exact sequence with Z as normal subgroup ⓘ
hasInvariant Seifert volume (in geometric cases) ⓘ
orbifold Euler characteristic of the base ⓘ
hasStructure decomposition into disjoint union of circles ⓘ
locally trivial circle fibration away from singular fibers ⓘ
introducedBy Herbert Seifert ⓘ
introducedInYear 1933 ⓘ
isSubsetOf Haken 3-manifolds (in many cases) ⓘ
prime 3-manifolds ⓘ
localModel S^1-bundle over a 2-dimensional disk for regular fibers ⓘ
fibered solid torus with nontrivial gluing for singular fibers ⓘ
namedAfter Herbert Seifert ⓘ
orientationProperty can be orientable or non-orientable ⓘ
specialCaseOf graph manifold ⓘ
supportsGeometry ilde{SL_2(R)}-geometry (in some cases) ⓘ
E^3-geometry (in some cases) ⓘ
Nil-geometry (in some cases) ⓘ
S^2 × R-geometry (in some cases) ⓘ
S^3-geometry (in some cases) ⓘ
usedIn JSJ decomposition of 3-manifolds ⓘ
classification of closed orientable 3-manifolds with infinite fundamental group ⓘ

How these facts were elicited

Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

Dehn surgery → canProduce → Seifert fibered spaces ⓘ
Hopf fibration → isExampleOf → Seifert fibration ⓘ
linked to: Seifert fibered spaces
JSJ decomposition → appliesTo → Haken 3-manifolds ⓘ
linked to: Seifert fibered spaces
S^2 × R geometry → relatedTo → Seifert fibered spaces ⓘ
Seifert fibered space → classifiedBy → Seifert invariants ⓘ
subject linked to: Seifert fibered spaces
linked to: Seifert fibered spaces