Remarks on the Liechti-Strenner’s examples having small dilatations. (English) Zbl 1465.37055
Summary: We show that the Liechti-Strenner’s example for the closed nonorientable surface in [L. Liechti and B. Strenner, Algebr. Geom. Topol. 20, No. 1, 451–485 (2020; Zbl 1437.57017)] 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 [L. Liechti and B. Strenner, Algebr. Geom. Topol. 20, No. 1, 451–485 (2020; Zbl 1437.57017)] 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.
MSC:
| 37E30 | Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces |
| 37B40 | Topological entropy |
| 57M60 | Group actions on manifolds and cell complexes in low dimensions |
| 57K20 | 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) |
Citations:
Zbl 1437.57017References:
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