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Algebraic Topology
· Problem 3E.4
Cohomology — Allen Hatcher
Mathematics — Topology · SO5-not-product
Problem
Using the cup product structure in
H
∗
(
S
O
(
5
)
;
Z
)
H^*(SO(5); \mathbb{Z})
H
∗
(
S
O
(
5
)
;
Z
)
, show that
S
O
(
5
)
SO(5)
S
O
(
5
)
is not homotopy equivalent to the product of any two CW complexes with nontrivial cohomology.
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