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Stefan Waldmann
Stefan Waldmann
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Consider the pullback of a (Hurewicz) fibration p:E-->B$p\colon E \longrightarrow B$ along any map f$f$ and let p'$p'$ denote the base change of p$p$ in the pullback. Suppose that H_(p), the induced homomorphism in singular homology (with coefficients in any field) of p, is surjective . Is it true that H_$H_*(p)$, the induced homomorphism in singular homology (p'with coefficients in any field) of $p$, is surjective . Is it true that $H_*(p')$ is also surjective? If not, when is this possible?

Consider the pullback of a (Hurewicz) fibration p:E-->B along any map f and let p' denote the base change of p in the pullback. Suppose that H_(p), the induced homomorphism in singular homology (with coefficients in any field) of p, is surjective . Is it true that H_(p') is also surjective? If not, when is this possible?

Consider the pullback of a (Hurewicz) fibration $p\colon E \longrightarrow B$ along any map $f$ and let $p'$ denote the base change of $p$ in the pullback. Suppose that $H_*(p)$, the induced homomorphism in singular homology (with coefficients in any field) of $p$, is surjective . Is it true that $H_*(p')$ is also surjective? If not, when is this possible?

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Jose Calcines
Jose Calcines
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Is surjectivity in singular homology stable under pullbacks?

Consider the pullback of a (Hurewicz) fibration p:E-->B along any map f and let p' denote the base change of p in the pullback. Suppose that H_(p), the induced homomorphism in singular homology (with coefficients in any field) of p, is surjective . Is it true that H_(p') is also surjective? If not, when is this possible?