Math 6510 • Differentiable Manifolds

View the 2-torus as

\[
T^2=\{(z,w)\in\mathbb{C}^2\mid |z|=|w|=1\}
\]

and let \(f : T^{2} \to T^{2}\) be defined by

\[
f(z,w)=(z^2,w^2)
\]

Prove that \(f\) is not homotopic to the identity.