Hatcher-Algebraic-Topology · Problem 2.2.23

Homology

Mathematics — Graph Theory · euler-characteristic

Problem

Show that if the closed orientable surface MgM_g of genus gg is a covering space of MhM_h, then g=n(h−1)+1g = n(h-1)+1 for some nn, namely, nn is the number of sheets in the covering. [Conversely, if g=n(h−1)+1g = n(h-1)+1 then there is an nn-sheeted covering Mg→MhM_g \to M_h, as we saw in Example 1.41.]

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