HOMEWORK 8
Exercise 1. Let f : M → N be a map between two oriented compact manifolds of
dimension n with fundamental classes [M] and [N], respectively. We say that f has
degree d if
f∗([M]) = d[N].
Prove that for every oriented compact manifold M of dimension n there is a map
f : M → Sn
of degree 1.
Exercise 2. Use cup product to show that RP3
is not homotopy equivalent to RP2
∨
S3
.
1