A Polygonal Perspective of Nielsen Reduction and the Chord Slide Groupoid
arXiv:1010.5275
Abstract
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 class of a surface with one boundary component, the resulting decomposition in general will not have a topological interpretation. In this survey, we discuss a variation called fatgraph Nielsen reduction which decomposes such a mapping class into elementary Nielsen transformations interpreted as rearrangements of polygon domains for described by systems of arcs in . These elementary moves generate the chord slide groupoid of , which we survey and describe in terms of generators and relations.
arXiv commentThis survey (minus minor corrections) was written for and published in the abstracts for the 57th Topology Symposium which took place in Okayama, JP \emph{2010}. It summarizes the contents of a talk of the same title which was given by the author at that conference on \emph{8/12/2010}