HOMEWORK 7 – 2022
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. (Hint: Find a geometric prescription and use the definition
of the fundamental class via local orientations.)
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