  Let $\Sigma$ be a surface with either boundary or marked points, equipped
with an arbitrary framing. In this note we determine the action of the
associated "framed mapping class group" on the homology of $\Sigma$ relative to
its boundary (respectively marked points), describing the image as the kernel
of a certain crossed homomorphism related to classical spin structures.
Applying recent work of the authors, we use this to describe the monodromy
action of the orbifold fundamental group of a stratum of abelian differentials
on the relative periods.
