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Let $F\rightarrow E\rightarrow S^n$, $n\geq 2$, be a fibration. Then we have the Wang exact sequence, $$ \cdots\rightarrow H_q(F)\rightarrow H_q(E)\rightarrow H_{q-n}(F)\rightarrow H_{q-1}(F)\rightarrow H_{q-1}(E)\rightarrow\cdots $$ (https://en.wikipedia.org/wiki/Spectral_sequence ("Wang sequence").

Does the above sequence exist if we would change the base space $S^n$ into an arbitrary homology sphere of dimension $n\geq 2$?

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