Is there a counterexample to the following assertion?:
Let $p_1:E_1\to B_1$ and $p_2:E_2\to B_2$ be fibrations with the same fiber $\mathbb S ^1$ such that $E_1$ and $E_2$ are homeomorphic (and both connected). Then $B_1$ and $B_2$ are homotopic.
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Sign up to join this communityIs there a counterexample to the following assertion?:
Let $p_1:E_1\to B_1$ and $p_2:E_2\to B_2$ be fibrations with the same fiber $\mathbb S ^1$ such that $E_1$ and $E_2$ are homeomorphic (and both connected). Then $B_1$ and $B_2$ are homotopic.
$S^1\times S^3$ fibers both over $S^3$ (obvious) and $S^1\times S^2$ (identity cross Hopf). BTW, you don't say "homotopic" about spaces.