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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.
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참고문헌 (16)
참고문헌 신청
J. W. Aaber / 2010 / Closed surface bundles of least volume / Algebr. Geom. Topol 10(4):2315~2342
W. Abikoff / 1980 / The real analytic theory of Teichm¨uller space / Lecture Notes in Mathematics 820
P. Arnoux / 1981 / Construction de diff´eomorphismes pseudo-Anosov / C. R. Acad. Sci. Paris S´er. I Math 292(1):75~78
M. Bauer / 1992 / An upper bound for the least dilatation / Trans. Amer. Math. Soc 330(1):361~370
A. J. Casson / 1988 / Automorphisms of surfaces after Nielsen and Thurston / Cambridge University Press
W. Abikoff / 1980 / The real analytic theory of Teichm¨uller space / Lecture Notes in Mathematics 820
P. Arnoux / 1981 / Construction de diff´eomorphismes pseudo-Anosov / C. R. Acad. Sci. Paris S´er. I Math 292(1):75~78
M. Bauer / 1992 / An upper bound for the least dilatation / Trans. Amer. Math. Soc 330(1):361~370
A. J. Casson / 1988 / Automorphisms of surfaces after Nielsen and Thurston / Cambridge University Press
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