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Hatcher-Algebraic-Topology
· Problem 3D.2
Cohomology
Mathematics — Graph Theory · cohomology-of-SO(n)
Problem
Using the CW structure on
S
O
(
n
)
SO(n)
S
O
(
n
)
, show that
π
1
S
O
(
n
)
≈
Z
2
\pi_1 SO(n) \approx \mathbb{Z}_2
π
1
S
O
(
n
)
≈
Z
2
for
n
≥
3
n \geq 3
n
≥
3
. Find a loop representing a generator, and describe how twice this loop is nullhomotopic.
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