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

2014/10/31 by Hyunshik Shin, Balázs Strenner · 1 citation
Mathematics · #math.GT #msc:37E30 #msc:57M99 #msc:15A18 #msc:11R32

paper · pdf · doi:10.2140/gt.2015.19.3645

published as Geom. Topol. 19 (2015) 3645-3656 · 12 pages, 1 figure

arxiv created 2015/04/03 · arxiv updated 2016/01/20

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.

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