Hatcher-Algebraic-Topology · Problem 1.3.12

The Fundamental Group

Mathematics — Graph Theory · covering-spaces

Problem

Let

a

and

b

be the generators of

\pi_1(S^1 \vee S^1)

corresponding to the two

S^1

summands. Draw a picture of the covering space of

S^1 \vee S^1

corresponding to the normal subgroup generated by

a^2

b^2

, and

(ab)^4

, and prove that this covering space is indeed the correct one.