Eriko Hironaka, Florida State University

Small dilatation pseudo-Anosov mapping classes coming from the simplest pseudo-Anosov braid.

In this talk we discuss the minimum dilatation pseudo-Anosov mapping classes coming from fibrations over the circle of a single 3-manifold, namely the mapping torus for the "simplest pseudo-Anosov braid". The dilatations that arise include the minimum dilatations for orientable mapping classes for genus $g=2,3,4,5,8$ as well as Lanneau and Thiffeault's conjectural minima for orientable mapping classes for $g=2,4 (\mod\ 6)$. The examples also show that the minimum dilatation for orientable mapping classes is strictly greater than the minimum dilatation for non-orientable ones when $g = 4,6,8$.

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