# For which $g,p$ does $\Sigma_{g,p}$ cover $\Sigma_{3,2}$?

I am preparing for my qualifying exams. There is an algebraic topology problem I don't know how to do it. Thanks a lot for your help.

Let $\Sigma_{g,p}$ denote the surface of genus $g$ with $p$ punctures. For what $g,p$ does $\Sigma_{g,p}$ cover $\Sigma_{3,2}$?

I know how to do this problem without punctures. Have no idea how to deal with the punctures.

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## migrated from mathematica.stackexchange.comJul 20 '12 at 21:32

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I once tried a problem like this using polar coordinates. The instructor said my argument was full of holes... –  Daniel Lichtblau Jul 20 '12 at 20:19