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 $f\colon X\to Y$ such that the fibers $f^{-1}(y)$ 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, vol. 1425, Berlin: Springer, pp. 91–101, doi:10.1007/BFb0083834, MR 1070579

External links

• http://mathoverflow.net/questions/53782/quasifibrations-and-homotopy-pullbacks
• http://mathoverflow.net/questions/60763/when-a-quasifibration-is-a-hurewicz-fibration
• http://www.lehigh.edu/~dmd1/tg516.txt