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.