Let $p\colon Y\to X$ be a finite covering map of path-connected "good" spaces (e.g. manifolds), and let $L$ be a local system on $Y$, and let $V$ be the corresponding representation of $\pi_1(Y)$. Then $p_*L$ is the local system on $X$ corresponding to the representation $\operatorname{Ind}_{\pi_1(Y)}^{\pi_1(X)} V$. Is there any standard notation for this local system? I was thinking something like $\operatorname{Ind}_Y^X L$.
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asked May 20, 2017 at 17:59
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10$\begingroup$ Why not $p_*L$? $\endgroup$– Daniel LittCommented May 20, 2017 at 18:08
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$\begingroup$ @DanielLitt For the use I have in mind, I have a whole plethora of covering maps, and it'd be a pain to have to name each one. $\endgroup$– Avi SteinerCommented May 20, 2017 at 18:11
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1$\begingroup$ Well, sorry, but that's the standard notation for it. $\endgroup$– Ben Webster ♦Commented May 21, 2017 at 2:26
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$\begingroup$ @BenWebster well, I guess that's my answer. $\endgroup$– Avi SteinerCommented May 21, 2017 at 3:24
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