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arXiv · 0710.2043

Roots, symmetries and conjugacy of pseudo-Anosov mapping classes

Jérôme Fehrenbach·Jérôme Los
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Abstract

An algorithm is proposed that solves two decision problems for pseudo-Anosov elements in the mapping class group of a surface with at least one marked fixed point. The first problem is the root problem: decide if the element is a power and in this case compute the roots. The second problem is the symmetry problem: decide if the element commutes with a finite order element and in this case compute this element. The structure theorem on which this algorithm is based provides also a new solution to the conjugacy problem.

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Jérôme Fehrenbach, Jérôme Los. 2007-10-10. Roots, symmetries and conjugacy of pseudo-Anosov mapping classes. https://arxiv.org/abs/0710.2043

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