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How can you see in this picture

of what order the covering maps be? Well I look for one with a degree of two and one with a degree of four. thanks a lot!

2 Answers 2

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Count vertices. [And forget about the rest: $a,b, a^2,a^{-1},...$]

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These are covering spaces for $S^1\vee S^1$. The edges labeled '$a$' map to one of the $S^1$'s and the edges labeled '$b$' map to the other. You only need to count the number of occurrences of '$a$', or '$b$'. For example, $(1)$ has two $a$'s and two $b$'s and is thus a double cover.

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    I just meant to count the $a$'s and $b$'s in the picture. The stuff in the brackets is telling you to which subgroup of $\mathbb{Z}* \mathbb{Z}$ the particular covering corresponds.2011-11-14