Hatcher-Algebraic-Topology · Problem 1.3.28

The Fundamental Group

Mathematics — Graph Theory · covering-spaces

Problem

Show that for a covering space action of a group

G

on a simply-connected space

Y

\pi_1(Y/G)

is isomorphic to

G

. [If

Y

is locally path-connected, this is a special case of part (c) of Proposition 1.40.]