On dilatation factors of braids on three strands
Abstract
In this work we present a natural surjective map from rigid braids in B_3 (in Garside sense) to SL_2(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 B_3.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2013
- DOI:
- 10.48550/arXiv.1307.6987
- arXiv:
- arXiv:1307.6987
- Bibcode:
- 2013arXiv1307.6987A
- Keywords:
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- Mathematics - Geometric Topology;
- Mathematics - Dynamical Systems;
- Mathematics - Group Theory;
- 20F36;
- 37E30
- E-Print:
- 13 pages, 5 figures