  The quantum Hall effect has been predicted and discovered in various
condensed-matter systems. A promising quantum material for such topological
effects is graphene. We report the numerical observation of a curvature-induced
spin-Hall effect in a monolayer graphene M\"obius strip. The solution of the
Dirac equation on the nontrivial and non-Euclidean manifold reveals that
despite the absence of a Hall current, a spin-Hall current is a natural
consequence for such a topology, as predicted from symmetry arguments.
