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 fibered links and comparing dilatations using the skein relation for Alexander polynomials.