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Hopf invariant

Homotopy invariant of maps between spheres
Thing invariant Q5900509
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Hopf invariant

Summary

Hopf invariant is an invariant[1]. It draws 31 Wikipedia views per month (invariant category, ranking #19 of 37).[2]

Key Facts

  • Hopf invariant is credited with the discovery of Heinz Hopf[3].
  • Hopf invariant's instance of is recorded as invariant[4].
  • Heinz Hopf is named after Hopf invariant[5].
  • Hopf invariant's time of discovery or invention is recorded as +1931-00-00T00:00:00Z[6].
  • Hopf invariant's Freebase ID is recorded as /m/0c15t_[7].
  • Hopf invariant's studied by is recorded as topology[8].
  • Hopf invariant's nLab ID is recorded as Hopf invariant[9].
  • Hopf invariant's Microsoft Academic ID is recorded as 2779442654[10].
  • Hopf invariant's Great Russian Encyclopedia portal ID is recorded as invariant-khopfa-6a72cb[11].
  • Hopf invariant's invariant under is recorded as homotopy[12].

Body

Works and Contributions

Hopf invariant is credited with the discovery of Heinz Hopf[3].

Why It Matters

Hopf invariant draws 31 Wikipedia views per month (invariant category, ranking #19 of 37).[2] It has Wikipedia articles in 5 language editions, a strong signal of global cultural recognition.[13]

References

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

Direct Wikidata claims

  1. [4] ↑ . wikidata.org.
  2. [3] ↑ . wikidata.org.
  3. [5] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . wikidata.org.
  6. [8] ↑ . wikidata.org.
  7. [9] ↑ . wikidata.org.
  8. [10] ↑ . wikidata.org.
  9. [11] ↑ . wikidata.org.
  10. [12] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [13] ↑ . Wikidata sitelinks. 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 invariant. Retrieved May 3, 2026, from https://4ort.xyz/entity/hopf-invariant
MLA “Hopf invariant.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/hopf-invariant.
BibTeX @misc{4ortxyz_hopf-invariant_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Hopf invariant}}, year = {2026}, url = {https://4ort.xyz/entity/hopf-invariant}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Hopf invariant — https://4ort.xyz/entity/hopf-invariant (retrieved 2026-05-03)

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