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Guangbo Xu
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Let $E\to B$ be a fibre bundle. The Leray-Hirsch theorem states under suitable assumptions, the cohomology of $E$ is an $H^*(B)$-module generated by suitable cohomology classes in $E$.

Is there any analogous results for the homology of $E$? Any reference?

Let $E\to B$ be a fibre bundle. The Leray-Hirsch theorem states under suitable assumptions, the cohomology of $E$ is an $H^*(B)$-module.

Is there any analogous results for the homology of $E$? Any reference?

Let $E\to B$ be a fibre bundle. The Leray-Hirsch theorem states under suitable assumptions, the cohomology of $E$ is an $H^*(B)$-module generated by suitable cohomology classes in $E$.

Is there any analogous results for the homology of $E$? Any reference?

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Guangbo Xu
  • 1.2k
  • 9
  • 16

Leray-Hirsch for HOMOLOGY?

Let $E\to B$ be a fibre bundle. The Leray-Hirsch theorem states under suitable assumptions, the cohomology of $E$ is an $H^*(B)$-module.

Is there any analogous results for the homology of $E$? Any reference?