On the minimum dilatation of braids on punctured discs

Abstract

We find the minimum dilatation of pseudo-Anosov braids on n-punctured discs for 3 <= n <= 8. This covers the results of Song-Ko-Los (n=4) and Ham-Song (n=5). The proof is elementary, and uses the Lefschetz formula.

16 pages, LaTeX with amsart style. Mathematica source code included.

References in corpus (4)

• Topology, Braids, and Mixing in Fluids
• A family of pseudo-Anosov braids with small dilatation
• Small dilatation pseudo-Anosov mapping classes coming from the simplest hyperbolic braid
• Closed surface bundles of least volume

Cited by in corpus (7)

• Pseudo-Anosov mapping classes not arising from Penner's construction
• The mathematics of taffy pullers
• Minimal dilatations of pseudo-Anosovs generated by the magic 3-manifold and their asymptotic behavior
• Estimating topological entropy from the motion of stirring rods
• Minimal pseudo-Anosov stretch factors on nonoriented surfaces
• Pseudo-Anosov maps with small stretch factors on punctured surfaces
• Least dilatation of pure surface braids