"Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931)

E679325

"Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931) is Heinz Hopf’s seminal paper in which he introduced the Hopf fibration, a foundational concept in algebraic topology describing a nontrivial mapping from the 3-sphere to the 2-sphere.

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Predicate Object
instanceOf mathematical research paper ⓘ
scientific article ⓘ
author Heinz Hopf ⓘ
citedFor geometric description of linked circles in S^3 ⓘ
original definition of the Hopf fibration ⓘ
classification classic paper in 20th-century mathematics ⓘ
codomain 2-sphere S^2 ⓘ
describes nontrivial mapping from 3-sphere to 2-sphere ⓘ
domain 3-sphere S^3 ⓘ
fiber circle S^1 ⓘ
field algebraic topology ⓘ
topology ⓘ
hasKeyResult construction of a map S^3 → S^2 with all fibers circles ⓘ
description of S^3 as union of linked circles (Hopf fibers) ⓘ
example of nontrivial element in π_3(S^2) ⓘ
historicalSignificance first explicit construction of the Hopf fibration ⓘ
foundational work in modern algebraic topology ⓘ
influenced development of fiber bundle theory ⓘ
development of homotopy theory ⓘ
introduces Hopf fibration ⓘ
introducesConcept linking of fibers in S^3 ⓘ
language German ⓘ
mainTopic Hopf fibration ⓘ
algebraic topology ⓘ
maps between spheres ⓘ
maps S^3 onto S^2 ⓘ
publicationYear 1931 ⓘ
relatedConcept Hopf invariant ⓘ
fiber bundle ⓘ
homotopy group of spheres ⓘ
principal circle bundle ⓘ
shows existence of nontrivial fiber bundle structure on S^3 over S^2 ⓘ
studies continuous maps from S^3 to S^2 ⓘ
titleTranslation On the mappings of the three-dimensional sphere onto the spherical surface ⓘ

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Heinz Hopf → notablePublication → "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931) ⓘ