2007/10/10 by Jérôme Fehrenbach, Fehrenbach, Jérôme, Jérôme Los +1
Computer Science · Mathematics · #37B10 #37D20 #37E30 #Digital Image Processing Techniques #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.48550/arxiv.0710.2043
openalex publication_date 2007/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.