Home › Entities › circle_bundle › Hopf fibration

Hopf fibration

fiber bundle of the 3-sphere over the 2-sphere, with 1-spheres as fibers
Thing circle_bundle Q1627604
Press Enter · cited answer in seconds

Hopf fibration

Summary

Hopf fibration is a circle bundle[1]. It has Wikipedia articles in 11 language editions, a strong signal of global cultural recognition.[2]

Key Facts

  • Hopf fibration's instance of is recorded as circle bundle[3].
  • Hopf fibration's instance of is recorded as mathematical concept[4].
  • Heinz Hopf is named after Hopf fibration[5].
  • Hopf fibration's Commons category is recorded as Hopf fibration[6].
  • Hopf fibration's maintained by WikiProject is recorded as WikiProject Mathematics[7].

Body

Definition and Type

Recorded instance of include circle bundle[3] and mathematical concept[4].

Origins

Heinz Hopf is named after Hopf fibration[5].

Why It Matters

Hopf fibration has Wikipedia articles in 11 language editions, a strong signal of global cultural recognition.[2] It is known by 12 alternative names across languages and contexts.[8]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] ↑ . wikidata.org.
  2. [4] ↑ . wikidata.org.
  3. [5] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikidata sitelinks. wikidata.org.
  2. [8] ↑ . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Hopf fibration. Retrieved May 3, 2026, from https://4ort.xyz/entity/hopf-fibration
MLA “Hopf fibration.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/hopf-fibration.
BibTeX @misc{4ortxyz_hopf-fibration_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Hopf fibration}}, year = {2026}, url = {https://4ort.xyz/entity/hopf-fibration}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Hopf fibration — https://4ort.xyz/entity/hopf-fibration (retrieved 2026-05-03)

Canonical URL: https://4ort.xyz/entity/hopf-fibration · Last refreshed:

Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 17d ago · Charp238 · 2026-07-07 view diff on Wikidata ↗
    Aliases → —
    Instance of → —
    Maintained by wikiproject → WikiProject Mathematics
    Stack exchange tag → https://mathoverflow.net/tags/hopf-fibration
    + 3 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-create:2||1 */ [[Property:P1482]]: https://mathoverflow.net/tags/hopf-fibration"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.