Remarks on the Liechti-Strenner's examples having small dilatations
Commun. Korean Math. Soc. 2020 Vol. 35, No. 4, 1299-1307
https://doi.org/10.4134/CKMS.c190365
Published online August 6, 2020
Printed October 31, 2020
Ji-Young Ham, Joongul Lee
Hongik University; Hongik University
Abstract : 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
Supported by : This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. NRF-2018R1A2B6005847). The second author was supported by 2018 Hongik University Research Fund.
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