Asymptotic Translation Length in the Curve Complex

Abstract

We show that when the genus and punctures of a surface are directly proportional by some rational number the minimal asymptotic translation length in the curve complex has behavior inverse to the square of the Euler characteristic. We also show that when the genus is fixed and the number of punctures varies the behavior is inverse to the Euler characteristic.

Errors corrected

Cited by in corpus (7)

• Fibrations of 3-manifolds and asymptotic translation length in the arc complex
• Small asymptotic translation lengths of pseudo-Anosov maps on the curve complex
• An upper bound on the asymptotic translation lengths on the curve graph and fibered faces
• On Translation Lengths of Anosov Maps on Curve Graph of Torus
• Minimal asymptotic translation lengths of Torelli groups and pure braid groups on the curve graph
• Combinatorics of tight geodesics and stable lengths
• Pseudo-Anosov mapping classes from pure mapping classes