Remarks on the Liechti-Strenner's examples having small dilatations.
Commun. Korean Math. Soc.
Published online August 6, 2020
Ji-Young Ham and Joongul Lee
Chung-Ang University, Hongik University
Abstract : Given a pseudo-Anosov homeomorphism $\psi$
We show that the Liechti-Strenner's example for the closed nonorientable surface in~\cite{LiechtiStrenner18} minimizes the dilatation within the class of pseudo-Anosov homeomorphisms with an orientable invariant foliation and all but the first coefficient of the characteristic polynomial of the action induced on the first cohomology nonpositive. We also show that the Liechti-Strenner's example of orientation-reversing homeomorphism for the closed orientable surface in~\cite{LiechtiStrenner18} minimizes the dilatation within the class of pseudo-Anosov homeomorphisms with an orientable invariant foliation and all but the first coefficient of the characteristic polynomial $p(x)$ of the action induced on the first cohomology nonpositive or all but the first coefficient of $p(x) (x \pm 1)^2$, $p(x) (x^2 \pm 1)$, or $p(x) (x^2 \pm x + 1)$ nonpositive.
Keywords : Minimal dilatation, Nonorientable surface, Liechti-Strenner, pseudo-Anosov stretch factors
MSC numbers : 37E30, 37B40, 57M60
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