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ThiKu
ThiKu
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Let us consider a homotopy fibre sequence of connected spaces $A\rightarrow B\rightarrow C$ and let $K$ be a fixed field. Assume that the homology $H_{\ast}(A, K)$ is trivial and that $C$ is a nilpotent space (but not simply connected).

Does $H_{\ast}(B, K)\rightarrow H_{\ast}(C, K)$ have to be an isomorphism ?

Let consider a homotopy fibre sequence of connected spaces $A\rightarrow B\rightarrow C$ and let $K$ be a fixed field. Assume that the homology $H_{\ast}(A, K)$ is trivial and that $C$ is nilpotent space (but not simply connected).

Does $H_{\ast}(B, K)\rightarrow H_{\ast}(C, K)$ an isomorphism ?

Let us consider a homotopy fibre sequence of connected spaces $A\rightarrow B\rightarrow C$ and let $K$ be a fixed field. Assume that the homology $H_{\ast}(A, K)$ is trivial and that $C$ is a nilpotent space (but not simply connected).

Does $H_{\ast}(B, K)\rightarrow H_{\ast}(C, K)$ have to be an isomorphism ?

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Let
Let
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Homologically trivial fibre

Let consider a homotopy fibre sequence of connected spaces $A\rightarrow B\rightarrow C$ and let $K$ be a fixed field. Assume that the homology $H_{\ast}(A, K)$ is trivial and that $C$ is nilpotent space (but not simply connected).

Does $H_{\ast}(B, K)\rightarrow H_{\ast}(C, K)$ an isomorphism ?