Math 6510 • Differentiable Manifolds

Let \(X\) be the topological space described on the Figure below: it is
obtained from the 2-dimensional square \(I^2\) by identifying segments with arrows (the
identification respects the orientation of edges determined by the arrows). Compute
\(\pi_1(X)\).

\emph{Diagram description: the square \(I^2\) has arrows on the left and right vertical
sides pointing upward, on the top and bottom horizontal sides pointing to the right,
and on the diagonal from the lower-left corner to the upper-right corner pointing
toward the upper-right corner. The arrowed segments are identified respecting these
orientations.}