Math 6520 • Algebraic Topology

Prove or disprove:
\begin{enumerate}

\item
For every \(d \in \mathbb{Z}\) there is a degree \(d\) map \(f_d : T^2 \to S^2\).


\item
For every \(d \in \mathbb{Z}\) there is a degree \(d\) map \(g_d : S^2 \to T^2\).

Here \(S^2\) is the 2-sphere and \(T^2 = S^1 \times S^1\) is the 2-dimensional torus.

\end{enumerate}