$p:E \rightarrow B$ is a fibration and $F$ is its fibre and $F_p$ its homotopy fibre. If $i:F \rightarrow F_p$ is the inclusion, is there a homotopy inverse $r$ of $i$ such that $r \circ i = id$?
Fibre and homotopy fibre
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algebraic-topology
homotopy-theory
fibration
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0I think in some cases it does. For example when $(F_p,F)$ satisfies homotopy extension property, $F$ is the deformation retract of $F_p$. – 2012-08-31