  We calculate the singular instanton homology with local coefficients for the
simplest n-strand braids in $S^1 \times S^2$ for all odd n, describing these
homology groups and their module structures in terms of the coordinate rings of
explicit algebraic curves. The calculation is expected to be equivalent to
computing the quantum cohomology ring of a certain Fano variety, namely a
moduli space of stable parabolic bundles on a sphere with n marked points.
