Algebraic Topology · Problem 3D.2

Cohomology — Allen Hatcher

Mathematics — Topology · fundamental-group-SO-n

Problem

Using the CW structure on

SO(n)

, show that

\pi_1 SO(n) \approx \mathbb{Z}_2

for

n \geq 3

. Find a loop representing a generator, and describe how twice this loop is nullhomotopic.