fundamental group

mathematical group of the homotopy classes of loops in a topological space
Thing topological_property Q662830
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fundamental group

Summary

fundamental group is a topological property[1]. It draws 287 Wikipedia views per month (topological_property category, ranking #2 of 9).[2]

Key Facts

  • fundamental group's instance of is recorded as topological property[3].
  • fundamental group's Library of Congress authority ID is recorded as sh85052367[4].
  • fundamental group's subclass of is recorded as homotopy group[5].
  • fundamental group's subclass of is recorded as deck transformation group[6].
  • fundamental group's Commons category is recorded as Fundamental group[7].
  • fundamental group's Freebase ID is recorded as /m/02z4l[8].
  • fundamental group's topic's main category is recorded as Category:Fundamental group[9].
  • fundamental group's Encyclopædia Britannica Online ID is recorded as topic/fundamental-group[10].
  • fundamental group's defining formula is recorded as {f[0,1]: \to X \mid \ f(0)=x_0=f(1)}[11].
  • fundamental group's MathWorld ID is recorded as FundamentalGroup[12].
  • fundamental group's Quora topic ID is recorded as Fundamental-Group[13].
  • fundamental group's nLab ID is recorded as fundamental group[14].
  • fundamental group's on focus list of Wikimedia project is recorded as Wikipedia:Vital articles/Level/4[15].
  • fundamental group's schematic is recorded as Fundamental group torus3.png[16].
  • fundamental group's maintained by WikiProject is recorded as WikiProject Mathematics[17].
  • fundamental group's Microsoft Academic ID is recorded as 159876591[18].
  • fundamental group's ProofWiki ID is recorded as Definition:Fundamental_Group[19].
  • fundamental group's Encyclopedia of Mathematics article ID is recorded as Fundamental_group[20].
  • fundamental group's PlanetMath ID is recorded as FundamentalGroup[21].
  • fundamental group's National Library of Israel J9U ID is recorded as 987007553155105171[22].
  • fundamental group's Group Properties article ID is recorded as Fundamental_group[23].
  • fundamental group's identity element is recorded as constant loop[24].
  • fundamental group's has operation is recorded as concatenation of loops[25].
  • fundamental group's Namuwiki ID is recorded as 기본군[26].
  • fundamental group's OpenAlex ID is recorded as C159876591[27].

Why It Matters

fundamental group draws 287 Wikipedia views per month (topological_property category, ranking #2 of 9).[2] It has Wikipedia articles in 25 language editions, a strong signal of global cultural recognition.[28]

References

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

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . github.com. Retrieved . github.com. Provenance: wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . Freebase Data Dumps. wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . Quora. wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . wikidata.org.
  14. [16] . wikidata.org.
  15. [17] . wikidata.org.
  16. [18] . wikidata.org.
  17. [19] . wikidata.org.
  18. [20] . wikidata.org.
  19. [21] . wikidata.org.
  20. [22] . National Library of Israel. wikidata.org.
  21. [23] . wikidata.org.
  22. [24] . wikidata.org.
  23. [25] . wikidata.org.
  24. [26] . wikidata.org.
  25. [27] . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [28] . 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). fundamental group. Retrieved May 3, 2026, from https://4ort.xyz/entity/fundamental-group
MLA “fundamental group.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/fundamental-group.
BibTeX @misc{4ortxyz_fundamental-group_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{fundamental group}}, year = {2026}, url = {https://4ort.xyz/entity/fundamental-group}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): fundamental group — https://4ort.xyz/entity/fundamental-group (retrieved 2026-05-03)

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