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\begin{document}

\hline

\vspace{0,25cm}
\begin{tabular}{ll}
{\Large Mathematisches Institut}\phantom{$3^P$}
\qquad\qquad\qquad\qquad\qquad\qquad\qquad & Eckerstr.~1 \\
der Universit"at Freiburg        & 79104 Freiburg i.~Br. \\
                                 & B"uro: (0761) 203-5540 \\
{\bf Prof.~Dr.~W.~Soergel}       & \\
{\bf Dr.~G.~H\"ohn}              &
\end{tabular}
\smallskip
\hline

\vspace{0,5cm}
\medskip


{\large \bf "Ubungen zur Topologie II}\hfill
{Wintersemester 2001/2002}\hfill {\large\bf Blatt 8}

\vspace{10mm}

\centerline{\bf Hausaufgaben, Abgabe bis 17.12.01 }


\vspace{5mm}

\noindent {\bf Aufgabe 1:}

\vspace{0,25cm}
\noindent Sei $(X,A)$ ein Raumpaar.
Gegeben $ z \in H_{p+q} (X,A)$ kommutiert das Diagramm
$$\begin{array}{ccc}
H^{p}(X,A) & \ra & H^{p} X\\
\cap z\downarrow & & \downarrow  \cap z\\
H_{q} X & \ra & H_{q} (X,A)
\end{array}$$


\vspace{4mm}
\noindent {\bf Aufgabe 2:}

\vspace{0,25cm}
\noindent Sei der topologische Raum
 $X$
eine aufsteigende Vereinigung
offener Teilmengen, $X=\bigcup_{i\in I} U_i$.
So gilt $H_q(X)=\varinjlim\; H_q(U_{i})$.


\vspace{4mm}
\noindent {\bf Aufgabe 3:}

\vspace{0,25cm}
\noindent Man bestimme die Kohomologieringe der quaternionalen
projektiven R"aume $\Bbb{P}^{n}\Bbb{H}$.




\vspace{4mm}

\noindent {\bf Aufgabe 4:}

\vspace{0,25cm}
\noindent Sei der Hausdorffraum $X$
eine aufsteigende Vereinigung
offener Teilmengen, $X=\bigcup_{i\in I} U_i$.
So gilt $H^q_c(X)=\varinjlim\; H^q_c(U_{i}).$



\vfill
\noindent {\small Sie finden alle "Ubungsbl"atter auch im Internet unter 
der Adresse
\newline
{\tt 
http://sunpool.mathematik.uni-freiburg.de/home/algebra/TopologieIISeite.html}}









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