The Torelli group of a surface S with one boundary component is defined
as the subgroup of the mapping class group of S which acts trivially on
the first homology of S.  This is in fact just the first of a sequence
of nested "higher Torelli" subgroups which serves as an approximation to
the mapping class group itself.  The study of the Torelli groups often
involves analysis of the Johnson homomorphisms which are certain abelian
quotients of the Torelli groups.  Morita has shown that the first
Johnson homomorphism lifts to a crossed homomorphism of the whole
mapping class group, while recently Morita and Penner have shown by use
of homology marked fatgraphs that it in fact lifts canonically to the
Torelli groupoid.  In this talk, I will report on recent  work (joint
with R. Penner and N. Kawazumi) in which canonical lifts of the higher
Johnson homomorphisms to the Torelli groupoid have been constructed.
The construction relies on Kawazumi's interpretation of the Johnson
homomorphisms in terms of Magnus expansions adapted to the Morita-Penner
perspective using fatgraphs.