Math 6510 • Differentiable Manifolds

Let \(X\) be the space obtained from a disk by identifying the boundary according
to the following diagram. Find the fundamental group \(\pi_1(X)\). Is \(X\) homeomorphic
to a closed surface? Explain.

\emph{Diagram description: a hexagonal disk with paired boundary labels. Reading
clockwise around the boundary, the labeled sides are
\(a^{-1},c,b,a,c^{-1},b^{-1}\); paired sides have matching labels with inverse
orientations.}