On dilatation factors of braids on three strands

2013/07/26 by Marta Aguilera, Aguilera, Marta
Mathematics · #20F36 #37E30 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.DS #math.GR #math.GT #msc:20F36 #msc:37E30

paper · pdf · doi:10.48550/arxiv.1307.6987

13 pages, 5 figures

arxiv created 2013/07/26 · arxiv updated 2013/07/29

Abstract

In this work we present a natural surjective map from rigid braids in B₃ (in Garside sense) to SL₂(N). This map provides an upper and a lower bound for the dilatation factor of a pseudo-Anosov 3-strand braid. These bounds only depend on the canonical length of the classical Garside structure of B₃.

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