Homework number 8
Do both exercises.
Exercise 18. Compute πk(RPn
) in terms of πk(Sn
).
Exercise 19. Let Y be a connected space with a base point yo such that the couple
(Y, {yo}) has the homotopy extension property. Then every continuous map f : Sk
→
Y can be extended to F : Dk+1
→ Y if and only if πk(Y, yo) = 0.
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