Math 6510 • Differentiable Manifolds

Consider the following two 2-complexes, \(A\) and \(B\), defined as identification
spaces of polygons, with side identifications as indicated (so all edges are
identified with each other).
\begin{center}
  \includegraphics[
    alt={Polygon A side-identification diagram from the original exam.},
    width=0.39\textwidth
  ]{GeomTopF2009-diagram-11A.png}
  \hfill
  \includegraphics[
    alt={Polygon B side-identification diagram from the original exam.},
    width=0.46\textwidth
  ]{GeomTopF2009-diagram-11B.png}
\end{center}
Is either space homotopy equivalent to a 1-complex?