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Results tagged with covering
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user 65800
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induced group actions and covering maps on Eilenberg-Maclane space
Then we have a covering map
$$
f:M\to M/\Sigma_k.
$$
From $f$, we have an induced map on the fundamental groups
$$
f_*:\pi_1(M)\to \pi_1(M/\Sigma_k).
$$
From $f_*$, we have an induced map on the Eilenberg-Maclane … spaces
$$
F: K(\pi_1(M),1)\to K(\pi_1(M/\Sigma_k),1).
$$
Question: Does there always exist an induced $\Sigma_k$-action on $K(\pi_1(M),1)$ such that $F$ is a covering map obtained by modulo this $\Sigma_k …
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