How to prove that a map is a Serre fibration? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T06:29:20Z http://mathoverflow.net/feeds/question/37608 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/37608/how-to-prove-that-a-map-is-a-serre-fibration How to prove that a map is a Serre fibration? Benoît Kloeckner 2010-09-03T12:41:42Z 2010-09-03T12:41:42Z <p>I want to prove that the homotopy groups of some topological space $B$ of interest to me (not a CW complex) are trivial. I have a strategy of proof that consists in introducing another space $E$ that is contractible, and easily comes with a continuous surjection $\pi :E\to B$. If I can prove that any continuous map $f:I^k\to B$ lifts to a continuous map $\tilde f : I^k\to E$, then I'm done.</p> <p>If I am not mistaken, this lifting property is true as soons as $\pi$ is a Serre fibration. Here is my question: are there classical way to prove such a thing, and were can I learn them (or simply learn about Serre fibrations)? Of course, any reference for the initial problem, which seems slightly weaker, is welcome too.</p> <p>I guess that I should be able to manage my case by hand, but I think it may be an opportunity to learn more mathematics.</p>