This is the first in a series of papers exploring the relationship between
the Rohlin invariant and gauge theory. We discuss the Casson-type invariant of
a 3-manifold with the integral homology of a torus, given by counting
projectively flat connections. We show that its mod 2 evaluation is given by
the triple cup product in cohomology, and so it coincides with a sum of Rohlin
invariants. Our counting argument makes use of a natural action of the first
cohomology on the moduli space of projectively flat connections; along the way
we construct perturbations that are equivariant with respect to this action.
Combined with the Floer exact triangle, this gives a purely gauge-theoretic
proof that Casson's homology sphere invariant reduces mod 2 to the Rohlin
invariant.Comment: Changed title to fit with succeeding papers in series. Added
reference to Turaev's wor
