Least dilatation of pure surface braids

Abstract

We study the minimal dilatation of pseudo-Anosov pure surface braids and provide upper and lower bounds as a function of genus and the number of punctures. For a fixed number of punctures, these bounds tend to infinity as the genus does. We also bound the dilatation of pseudo-Anosov pure surface braids away from zero and give a constant upper bound in the case of a sufficient number of punctures.

16 pages, 9 figures, with an appendix by Marissa Loving and Hugo Parlier

References in corpus (2)

• A family of pseudo-Anosov braids with small dilatation
• Lower bound for the Perron-Frobenius degrees of Perron numbers

Cited by in corpus (2)

• Pseudo-Anosov maps with small stretch factors on punctured surfaces
• Pseudo-Anosov homeomorphisms of punctured non-orientable surfaces with small stretch factor