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\begin{center}\begin{large}\textbf{Math 131 - Problem Set 10\\
Due Tuesday, Nov 27}\end{large}\end{center}



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\noindent From Munkres: 58.2, 59.4, 60.5, 79.1, 79.2, 79.4

\begin{enumerate}

\item Let $X$ be the figure eight space, with base point $x_0$ where the two circles are glued. Let $a$ and $b$ be the two free generators of $\pi_1(X, x_0)$. 

\begin{enumerate}
\item What are the connected degree two coverings of $X$ up to equivalence? Draw them! Make sure to label and orient the edges like we did in class.
\item For each covering that you drew in (a), give a list generators for the corresponding subgroup of $\pi_1(X, x_0)$.
\end{enumerate}

\item (Just for fun -- not to be graded) Do the same as in problem 1 for the degree 3 coverings of $X$.

\end{enumerate}





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