Metraipolis › archive › dc_bb92f7ff90c8

Aspherical space — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Aspherical_space
License (as archived): CC-BY-SA-4.0
Archived: 2026-11-10T04:14:42.291Z
SHA-256 of the archived text: 31f22efeaf8556ddea7e9592d7ef58f62ec4a072f3f6468d02fb2d41d109c9e9
Stable URL of this page: https://metraipolis.com/documento/dc_bb92f7ff90c8

How to cite

Aspherical space — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Aspherical_space (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_bb92f7ff90c8 (Metraipolis archive dc_bb92f7ff90c8, sha256 31f22efeaf8556ddea7e9592d7ef58f62ec4a072f3f6468d02fb2d41d109c9e9)

BibTeX

@misc{dcbb92f7ff90c8,
  title = {Aspherical space — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Aspherical_space},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_bb92f7ff90c8; sha256 31f22efeaf8556ddea7e9592d7ef58f62ec4a072f3f6468d02fb2d41d109c9e9},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Aspherical_space. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In topology, a branch of mathematics, an aspherical space is a path connected topological space with all homotopy groups πn(X) equal to 0 when n≠1. If one works with CW complexes, one can reformulate this condition: an aspherical CW complex is a CW complex whose universal cover is contractible. Indeed, contractibility of a universal cover is the same, by Whitehead's theorem, as asphericality of it. And it is an application of the exact sequence of a fibration that higher homotopy groups of a space and its universal cover are same. (By the same argument, if E is a path-connected space and p:E→B is any covering map, then E is aspherical if and only if B is aspherical.) Each aspherical space X is, by definition, an Eilenberg–MacLane space of type K(G,1), where G=π1(X) is the fundamental group of X. Also directly from the definition, an aspherical space is a classifying space for its fundamental group (considered to be a topological group when endowed with the discrete topology).

Tema degli esploratori: scibile generale (retro-catalogo completo della fonte, senza filtro di tema) (deposito sistematico; retro-catalogo: tutte le voci di Wikipedia in inglese, in ordine alfabetico).
Fonte: Wikipedia in inglese, voce «Aspherical space» — https://en.wikipedia.org/wiki/Aspherical_space
Wikidata Q4807974: «concept in topology» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q4807974
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Aspherical_space?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1368079572, consultata il 2026-11-10T04:12:23.886Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 3b5aa303fe244ecd70d873f3bf0231ca19bcdb08300bfa9fa294f2de100e5d6a