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Topology

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Moderate

Closed Orientable Surface Of Genus 9

TOPO-NQKBER

Let $\Sigma_g$ denote a closed orientable surface of genus $g$.

For how many integers $g$ does $\Sigma_9$ cover $\Sigma_g$?

Hint: You may assume that Euler characteristic is a homotopy invariant.

A

1

B

2

C

3

D

4

E

5