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edit approved Mar 18, 2019 at 17:08
Peter Mortensen
edit approved Mar 18, 2019 at 17:08
Peter Mortensen
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homology Homology of the fiber

Let $f:X\rightarrow Y $ be a fibration (with fiber $F$) between simply connected spaces such that $H_{\ast}(f):H_{\ast}(X,\mathbb{Z})\rightarrow H_{\ast}(Y,\mathbb{Z})$ is an isomorphism for $\ast\leq n$, is

Is it true that the reduced homology of the fiber is $\tilde{H}_{\ast}(F,\mathbb{Z})=0$ for $\ast\leq n$  ?

homology of the fiber

Let $f:X\rightarrow Y $ be a fibration (with fiber $F$) between simply connected spaces such that $H_{\ast}(f):H_{\ast}(X,\mathbb{Z})\rightarrow H_{\ast}(Y,\mathbb{Z})$ is an isomorphism for $\ast\leq n$, is it true that the reduced homology of the fiber is $\tilde{H}_{\ast}(F,\mathbb{Z})=0$ for $\ast\leq n$  ?

Homology of the fiber

Let $f:X\rightarrow Y $ be a fibration (with fiber $F$) between simply connected spaces such that $H_{\ast}(f):H_{\ast}(X,\mathbb{Z})\rightarrow H_{\ast}(Y,\mathbb{Z})$ is an isomorphism for $\ast\leq n$

Is it true that the reduced homology of the fiber is $\tilde{H}_{\ast}(F,\mathbb{Z})=0$ for $\ast\leq n$?

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homology of the fiber

Let $f:X\rightarrow Y $ be a fibration (with fiber $F$) between simply connected spaces such that $H_{\ast}(f):H_{\ast}(X,\mathbb{Z})\rightarrow H_{\ast}(Y,\mathbb{Z})$ is an isomorphism for $\ast\leq n$, is it true that the reduced homology of the fiber is $\tilde{H}_{\ast}(F,\mathbb{Z})=0$ for $\ast\leq n$ ?