2 citations · 6 across the 7 of their papers we have counts for
7 papers
A Polygonal Perspective of Nielsen Reduction and the Chord Slide Groupoid
Alex James Bene
Nielsen reduction is an algorithm which decomposes any automorphism of a free group into a product of elementary Nielsen transformations. While this may be applied to a mapping cla…
Finite type invariants and fatgraphs
Jorgen Ellegaard Andersen, Alex James Bene, Jean-Baptiste Meilhan +1
We define an invariant of pairs M,G, where M is a 3-manifold obtained by surgery on some framed link in the cylinder , S is a connected surface with at lea…
Mapping Class Factorization via Fatgraph Nielsen Reduction
Alex James Bene
The mapping class group of a genus surface with one boundary component is known to have a simple yet infinite presentation with generators given by elementary moves c…
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…
Groupoid Extensions of Mapping Class Representations for Bordered Surfaces
Jorgen Ellegaard Andersen, Alex James Bene, R. C. Penner
The mapping class group of a surface with one boundary component admits numerous interesting representations including as a group of automorphisms of a free group and as a group of…
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…