
\begin{tabular}{|p{0.7in}|p{1.7in}|p{1.7in}|p{1.7in}|}
\hline $M$ & $\pi_1(M)$ & $H_k(M)$ & $\HdR^k(M)$ \\
\hline

\hline pt., $D^n$, $\R^n$
	& 0
	&	$\begin{cases}
		\Z[\textrm{pt.}], & k=1\\
		0, & k>0 \\
		\end{cases}$
	& {} \\

\hline $\S^n$
	&	$\begin{cases}
		\Z[\alpha], & n=1\\
		0, & n>1 \\
		\end{cases}$
	&	$\begin{cases}
		\Z[\textrm{pt.}], & k=0\\
		0,       & k \ne 0, n \\
		\Z[\S^n], & k=n\\
		\end{cases}$
	& {} \\

\hline $T^2$
	&
		\begin{eqnarray*}
			&&\pig{a,b|aba^{-1}b^{-1}=1} \\
			&&\Z[a]\oplus\Z[b]
		\end{eqnarray*}
	& {}
	& {} \\

\hline $T^3$
	& {}
	& {}
	& {} \\

\hline $T^n$
	& {}
	& {}
	& {} \\

\hline $nT^2$
	& {}
	& {}
	& {} \\

\hline $\R\P^2$
	& {}
	& {}
	& {} \\

\hline $\R\P^n$
	& $\pig{a|a^2=1} = \Z_2[\alpha]$
	& {}
	& {} \\

\hline $\C\P^n$
	& {}
	& {}
	& {} \\

\hline K.B.
	& {}
	& {}
	& {} \\

\hline $nP^2$
	& {}
	& {}
	& {} \\

\hline $X \times Y$
	& {}
	& {}
	& {} \\

\hline $M1 \wedge M_2$
	& {}
	& {}
	& {} \\

\hline $M1 \# M_2$
	& {}
	& {}
	& {} \\

\hline $\coprod X_\alpha$   
	& {}
	& {}
	& {} \\
\hline Graph $\Gamma$
	& {}
	& {}
	& {} \\

\hline Conn'd $n$-manifold
	& {}
	& {}
	& {} \\

\hline Path-connected space
	& {}
	& {}
	& {} \\

\hline
\end{tabular}
