Math 6510 • Differentiable Manifolds

\begin{enumerate}
\item[(a)] Define the concepts of chain morphisms and chain homotopies.
\item[(b)] Show that every map \(S^2\to T^2\) from the 2-sphere to the 2-torus is
null-homotopic.
\item[(c)] Write down explicit cellular chain complexes \(C(S^2)\) and \(C(T^2)\) for
\(S^2\) and \(T^2\) and a chain morphism \(\Phi:C(S^2)\to C(T^2)\) which is not chain
homotopic to a chain morphism representing a constant map.
\end{enumerate}