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Homotopy theory, homological algebra, algebraic treatments of manifolds.
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In a fibration, can a deformation retraction of the base be lifted to the total space?
Given a fibration $p:E \rightarrow B$ and if $A$ is a deformation retract of $B$. Is it true that $p^{-1}(A)$ is a deformation retract of $E$?. If this is not true, can some conditions be imposed on $ …