Quasi-fibration
In algebraic topology, a branch of mathematics, a quasi-fibration, introduced by Albrecht Dold and René Thom, is a continuous map of topological spaces such that the fibers are homotopy equivalent to the homotopy fiber of f via the canonical map.
Every fibration is a quasi-fibration, but the converse is not true. For instance, the projection of the letter L to its base interval is a quasi-fibration (all fibers are contractible), but not a fibration.
References
- Dold, Albrecht; Thom, René (1958), "Quasifaserungen und unendliche symmetrische Produkte", Annals of Mathematics, Second Series, 67: 239–281, doi:10.2307/1970005, ISSN 0003-486X, JSTOR 1970005, MR 0097062
- May, J.Peter (1990), "Weak equivalences and quasifibrations" (PDF), Groups of self-equivalences and related topics (Montreal, PQ, 1988), Lecture Notes in Mathematics, 1425, Berlin: Springer, pp. 91–101, doi:10.1007/BFb0083834, MR 1070579
External links
- Quasifibrations and homotopy pullbacks
- When a quasifibration is a Hurewicz fibration?
- http://www.lehigh.edu/~dmd1/tg516.txt
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