Characterizing right-veering homeomorphisms of the punctured torus via the Burau representation
Davie, Emille Kennae
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We classify right-veering homeomorphisms of the once-punctured torus using the Burau rep-resentation of the 3-strand braid group. We show that reducible and periodic mapping classes inB3 can be identified as right-veering by consideration of the reduced version of the Burau rep-resentation. Given a pseudo-Anosov mapping class in B3, we construct an algorithm for findingits fractional Dehn twist coefficient which determines if this mapping class is right-veering, left-veering, or neither.