Math 6510 • Differentiable Manifolds

\begin{enumerate}
\item Let \(X\) be a CW-complex and \(A\) a sub-complex. Assume that all cells of \(X-A\)
have dimension \(>n\). If \(X\) retracts to \(A\) show that \(\pi_n(X)=\pi_n(A)\).
\item Show that \(\mathbb{R}P^n\) does not retract to \(\mathbb{R}P^k\) if \(k<n\).
\end{enumerate}