Journal article

Minimal pseudo-Anosov stretch factors on nonoriented surfaces

  • Liechti, Livio Department of Mathematics, University of Fribourg, Switzerland
  • Strenner, Balázs School of Mathematics, Georgia Institute of Technology, Atlanta, USA
Published in:
  • Algebraic & Geometric Topology. - 2020, vol. 20, no. 1, p. 451–485
English 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.
Faculté des sciences et de médecine
Département de Mathématiques
  • English
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