New answers tagged classifying-spaces
1
vote
Vector bundles with equivalent sphere bundles
If there is a diffeomorphism $f: E_0 \cong E_1$ so that $f$ is homotopic to the identity on $B$ (via the homotopy equivalences $E_0, E_1 \cong B$), then $E_0, E_1$ are stably equivalent as vector ...
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Classifying space of a category / classifying space of a group
For a category $\mathsf{C}$, $\mathrm{Nerve}(\mathsf{C})$ has an $n$-simplex for each chain of $n$ composable morphisms in $\mathsf{C}$:
$$
x_0\xrightarrow{m_1}x_1\xrightarrow{m_2} x_2 \...
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