Hatcher-Algebraic-Topology · Problem 1.A.4

The Fundamental Group

Mathematics — Graph Theory · graphs-and-free-groups

Problem

X

is a finite graph and

Y

is a subgraph homeomorphic to

S^1

and containing the basepoint

x_0

, show that

\pi_1(X, x_0)

has a basis in which one element is represented by the loop

Y