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\begin{document}
\pagestyle{fancy} \lhead{1301 Topology II, Assignment 5} \rhead{Due
  date: April 8, 2013} \cfoot{}
\noindent {\bf Reading:} Hatcher \S 3.1 and beginning of 3.2.

\begin{exercise}
Give an explicit singular cocycle which represents the generator for $H^1(S^1,\ZZ)$.  Do similarly for $H^n(S^n,\ZZ)$.
\end{exercise}

\begin{exercise}
Hatcher, Section 2.2 Exercises 14, 15, 19.
\end{exercise}


\begin{exercise}
Hatcher, Section 3.1 Exercises 1, 3, 6.
\end{exercise}

\begin{exercise}
Using the cup product, show that every map $S^2\to T^2$ has degree zero.
\end{exercise}


\end{document}
