%0 Generic %1 Bene2010 %A Bene, Alex James %D 2010 %K chord mapping nielsen polygonal surfaces %T A Polygonal Perspective of Nielsen Reduction and the Chord Slide Groupoid %U http://arxiv.org/abs/1010.5275 %X 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 $S_g,1$ 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 $S_g,1$ described by systems of arcs in $S_g,1$. These elementary moves generate the chord slide groupoid of $S_g,1$, which we survey and describe in terms of generators and relations.

@misc{Bene2010, 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 $S_{g,1}$ 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 $S_{g,1}$ described by systems of arcs in $S_{g,1}$. These elementary moves generate the chord slide groupoid of $S_{g,1}$, which we survey and describe in terms of generators and relations. }, added-at = {2010-10-31T14:26:23.000+0100}, author = {Bene, Alex James}, biburl = {https://www.bibsonomy.org/bibtex/2165731163a4f244408f873b610bafa8f/uludag}, description = {A Polygonal Perspective of Nielsen Reduction and the Chord Slide Groupoid}, interhash = {c34bc74b575945c19eb3295d7db82c1b}, intrahash = {165731163a4f244408f873b610bafa8f}, keywords = {chord mapping nielsen polygonal surfaces}, note = {cite arxiv:1010.5275 Comment: 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}}, timestamp = {2010-10-31T14:26:23.000+0100}, title = {A Polygonal Perspective of Nielsen Reduction and the Chord Slide Groupoid}, url = {http://arxiv.org/abs/1010.5275}, year = 2010 }