A Polygonal Perspective of Nielsen Reduction and the Chord Slide Groupoid
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.
Keywords
Cite
@article{arxiv.1010.5275,
title = {A Polygonal Perspective of Nielsen Reduction and the Chord Slide Groupoid},
author = {Alex James Bene},
journal= {arXiv preprint arXiv:1010.5275},
year = {2010}
}
Comments
This 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}