Minimal Penner dilatations on nonorientable surfaces

Livio Liechti; Balázs Strenner

doi:10.1142/s1793525320500119

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arXiv · 1807.08940

Minimal Penner dilatations on nonorientable surfaces

Livio Liechti·Balázs Strenner

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Abstract

For any nonorientable closed surface, we determine the minimal dilatation among pseudo-Anosov mapping classes arising from Penner's construction. We deduce that the sequence of minimal Penner dilatations has exactly two accumulation points, in contrast to the case of orientable surfaces where there is only one accumulation point. One of our key techniques is representing pseudo-Anosov dilatations as roots of Alexander polynomials of fibred links and comparing dilatations using the skein relation for Alexander polynomials.

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BibTeX RIS

Livio Liechti, Balázs Strenner. 2023-02-28. Minimal Penner dilatations on nonorientable surfaces. https://doi.org/10.1142/s1793525320500119

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