Odd-genus normalized limit conjecture for orientation-reversing stretch factors

Let SgS_g be the closed orientable surface of genus gg, and let δrev+(Sg)\delta^+_{\mathrm{rev}}(S_g) be the minimal stretch factor among orientation-reversing pseudo-Anosov homeomorphisms of SgS_g with orientable invariant foliations. The notation gg\to\infty with gg odd means that the limit is taken through odd genera.

Odd-genus normalized limit conjecture.

limgg odd(δrev+(Sg))g=1+2=silver ratio.\lim_{\substack{g\to\infty\\ g\text{ odd}}}(\delta^+_{\mathrm{rev}}(S_g))^g=1+\sqrt{2}=\text{silver ratio}.

The source derives this as a predicted consequence of the odd-genus polynomial formula. The limit remains open because that formula is itself conjectural.

Sources & referencesView supporting material

Primary source

Livio Liechti and Balázs Strenner, “Minimal pseudo-Anosov stretch factors on nonoriented surfaces”, arXiv:1806.00033 (2020).

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