The mapping class group is the group of (isotopy classes of)
orientation-preserving homeomorphisms of a surface. We will discuss some
new 3-dimensional bordism invariants of certain subgroups of the mapping
class group. In particular, these are invariants of the Johnson filtration
of the mapping class group. We will discuss a new representation in terms
of spin bordism which combines into a single homomorphism all of the
information given by many of the well-known representations, including
the Johnson homomorphism, Birman-Craggs homomorphism, and Morita
homomorphism.