HOMEWORKS 9 AND 10 – 2020
Exercise 1. Let (X, A) be a pair of CW-complexes with A contractible. Use the
extension lemma to prove that A is a retract of X.
Exercise 2. Let G be an Abelian group and let n ≥ 2 be an integer. Construct a
CW-complex X with homotopy groups πn(X) = G and πi(X) = 0 for i = n. Try to
prove that any two such CW-comlexes are homotopy equivalent.
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