Show that the index of $A$ in $\pi_1(Y, f(x))$ is finite and divides $m$.

Asked Apr 23 '13 at 21:56

Active Apr 24 '13 at 00:09

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I am studying for a qualifying exam problem and I am having difficulties with this problem. I feel that the solution involves lifting properties, but I am not quite sure how to start.

Let $X$ and $Y$ be closed connected oriented 2ñmanifolds, and let $f : X \rightarrow Y$ be a map of degree $m \neq 0.$ Let $A$ denote the image of $\pi_1f : \pi_1(X, x) \rightarrow \pi_1(Y, f(x)).$ By considering the cover of $Y$ corresponding to $A$, show that the index of $A$ in $\pi_1(Y, f(x))$ is finite and divides $m$.

Thank you for any help.

edited Apr 24 '13 at 00:09

Berci

90,745

asked Apr 23 '13 at 21:56

Kristie

Show that the index of $A$ in $\pi_1(Y, f(x))$ is finite and divides $m$.

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