Minimal Penner dilatations on nonorientable surfaces

Abstract

For any nonorientable closed surface, we determine the minimal dilatation among pseudo-Anosov mapping classes arising from Penner's construction. We deduce that the sequence of minimal Penner dilatations has exactly two accumulation points, in contrast to the case of orientable surfaces where there is only one accumulation point. One of our key techniques is representing pseudo-Anosov dilatations as roots of Alexander polynomials of fibred links and comparing dilatations using the skein relation for Alexander polynomials.

30 pages, 17 figures

References in corpus (2)

• Algebraic degrees of pseudo-Anosov stretch factors
• Minimal dilatation in Penner's construction

Cited by in corpus (2)

• Minimal pseudo-Anosov stretch factors on nonoriented surfaces
• Pseudo-Anosov maps with small stretch factors on punctured surfaces