Hatcher-Algebraic-Topology · Problem 1.3.22

The Fundamental Group

Mathematics — Graph Theory · covering-spaces

Problem

Given covering space actions of groups

G_1

X_1

and

G_2

X_2

, show that the action of

G_1 \times G_2

X_1 \times X_2

defined by

(g_1, g_2)(x_1, x_2) = (g_1(x_1), g_2(x_2))

is a covering space action, and that

(X_1 \times X_2)/(G_1 \times G_2)

is homeomorphic to

X_1/G_1 \times X_2/G_2