Homology fibration

A map of topological spaces $ f: X \rightarrow Y$ is a homology fibration if, for every $ y \in Y$, the natural map $ f^{-1}(y)
\rightarrow Pf_y$ from the fiber over $ y$ to the homotopy fiber over $ y$ induces an isomorphism on homology groups. By a theorem of McDuff and Segal, this is implied, for instance, by the condition that for sufficiently small neighborhoods $ U$ of $ y$, the inclusion $ f^{-1}(y)
\rightarrow f^{-1}(U)$ induces an isomorphism on homology.

Jeffrey Herschel Giansiracusa 2005-06-27