Welcome to mathimatikoi.org forum; Enjoy your visit here.

Degree of map

Algebraic Topology
Post Reply
Papapetros Vaggelis
Community Team
Community Team
Articles: 0
Posts: 426
Joined: Mon Nov 09, 2015 1:52 pm

Degree of map

#1

Post by Papapetros Vaggelis » Tue Nov 10, 2015 1:11 pm

Let \(\displaystyle{p}\) be a polynomial function on \(\displaystyle{\mathbb{C}}\) which has no root on \(\displaystyle{S^{1}}\) .

Show that the number of roots of the equation \(\displaystyle{p(z)=0\,,z\in\mathbb{C}}\) with \(\displaystyle{|z|<1}\)

is the degree of the map \(\displaystyle{\bar{p}:S^{1}\longrightarrow S^{1}}\) specified by \(\displaystyle{\bar{p}(z)=\dfrac{p(z)}{|p(z)|}}\) .
Post Reply