1 citations · 1 across the 2 of their papers we have counts for
2 papers
math.GT2008
A Chord Diagrammatic Presentation of the Mapping Class Group of a Once Bordered Surface
Alex James Bene
The Ptolemy groupoid is a combinatorial groupoid generated by elementary moves on marked trivalent fatgraphs with three types of relations. Through the fatgraph decomposition of Te…
math.GT2007★ 1 cited
Canonical lifts of the Johnson homomorphisms to the Torelli groupoid
Alex James Bene, Nariya Kawazumi, R. C. Penner
We prove that every trivalent marked bordered fatgraph comes equipped with a canonical generalized Magnus expansion in the sense of Kawazumi. This Magnus expansion is used to give…