#### Volume 20, issue 1 (2020)

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Minimal pseudo-Anosov stretch factors on nonoriented surfaces

### Livio Liechti and Balázs Strenner

Algebraic & Geometric Topology 20 (2020) 451–485
##### Abstract

We determine the smallest stretch factor among pseudo-Anosov maps with an orientable invariant foliation on the closed nonorientable surfaces of genus $4$, $5$, $6$, $7$, $8$, $10$, $12$, $14$, $16$, $18$ and $20$. We also determine the smallest stretch factor of an orientation-reversing pseudo-Anosov map with orientable invariant foliations on the closed orientable surfaces of genus $1$, $3$, $5$, $7$, $9$ and $11$. As a byproduct, we obtain that the stretch factor of a pseudo-Anosov map on a nonorientable surface or an orientation-reversing pseudo-Anosov map on an orientable surface does not have Galois conjugates on the unit circle. This shows that the techniques that were used to disprove Penner’s conjecture on orientable surfaces are ineffective in the nonorientable cases.

##### Keywords
small stretch factor, minimal dilatation, pseudo-Anosov map, dilatation, Penner's construction, nonorientable surface
##### Mathematical Subject Classification 2010
Primary: 57M20
Secondary: 11C08, 37E30, 57M99