Pseudo-Anosov mapping classes not arising from Penner's construction

Abstract

We show that Galois conjugates of stretch factors of pseudo-Anosov mapping classes arising from Penner's construction lie off the unit circle. As a consequence, we show that for all but a few exceptional surfaces, there are examples of pseudo-Anosov mapping classes so that no power of them arises from Penner's construction. This resolves a conjecture of Penner.

12 pages, 1 figure

References in corpus (2)

• Probing mapping class groups using arcs
• Algebraic degrees of stretch factors in mapping class groups

Cited by in corpus (8)

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• Salem number stretch factors and totally real fields arising from Thurston's construction
• Minimal pseudo-Anosov stretch factors on nonoriented surfaces
• On Translation Lengths of Anosov Maps on Curve Graph of Torus
• Least dilatation of pure surface braids
• Minimal dilatation in Penner's construction
• A construction of pseudo-Anosov homeomorphisms using positive twists
• Uniform difference between the length spectra of Out(F2) and the genus two handlebody group