Characterizing right-veering homeomorphisms of the punctured torus via the Burau representation

Details Characterizing right-veering homeomorphisms of the punctured torus via the Burau representation Characterizing right-veering homeomorphisms of the punctured torus via the Burau representation

2008-04-29

arxiv.org/abs/0804.4694v2

Mathematics

Geometric Topology

12 pages, 12 figures

Scientific paper

We classify right-veering homeomorphisms of the once-punctured torus using the Burau representation of the 3-strand braid group. We show that reducible and periodic mapping classes in B_3 can be identified as right-veering by consideration of the reduced version of the Burau representation. Given any element beta in B_3, we give a method to quickly determine its action on the generators of the fundamental group of the 3-times punctured disk. This action which determines whether beta is right-veering, left-veering, or neither.

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