Hatcher-Algebraic-Topology · Problem 1.A.10

The Fundamental Group

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

Problem

Let

X

be the wedge sum of

n

circles, with its natural graph structure, and let

\tilde{X} \to X

be a covering space with

Y \subset \tilde{X}

a finite connected subgraph. Show there is a finite graph

Z \supset Y

having the same vertices as

Y

, such that the projection

Y \to X

extends to a covering space

Z \to X