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Conjugacy invariants for Brouwer mapping classes

Published online by Cambridge University Press:  08 March 2016

JULIETTE BAVARD*
Affiliation:
Sorbonne Universités, UPMC Université Paris 06, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Université Paris Diderot, Sorbonne Paris Cité, F-75005, Paris, France email juliette.bavard@imj-prg.fr
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Abstract

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We give new tools for homotopy Brouwer theory. In particular, we describe a canonical reducing set called the set of walls, which splits the plane into maximal translation areas and irreducible areas. We then focus on Brouwer mapping classes relative to four orbits and describe them explicitly by adding a tangle to Handel’s diagram and to the set of walls. This is essentially an isotopy class of simple closed curves in the cylinder minus two points.

Type
Research Article
Copyright
© Cambridge University Press, 2016 

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