Canonical extensions of Morita homomorphisms to the Ptolemy groupoid (Q431033)

In the article under review, the author studies the Johnson filtration for the mapping class group from the point of view of the Ptolemy groupoid. The Ptolemy groupoid is a combinatorial generalization of the mapping class group, and is defined as the fundamental groupoid of a certain space of marked fat-graphs. In the setup, the author is able to construct tautological and infinitesimal extensions of the Morita homomorphisms, as well as infinitesimal extensions of the Johnson homomorphisms.