Dynamics of pseudo-Anosov maps and topology of fibered 3-manifolds

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04875
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Osaka University
• Principal Investigator: Kin Eiko 大阪大学, 理学研究科, 准教授 (80378554)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 写像類群 / ３次元双曲多様体 / 擬アノソフ / 位相的エントロピー / 曲線複体 / 群の不変順序 / モノドロミー / 双曲体積

Outline of Final Research Achievements

We studied two invariants of pseudo-Anosov elements in the mapping class group. One is the　entropy which is the translation length of the pseudo-Anosov element on the Teichmuller space. The other is the asymptotic translation length of the pseudo-Anosov element on the curve complex. We proved that the minimal asymptotic translation length among pseudo-Anosov elements in the hyperelliptic mapping class group of genus g behaves like 1/g^2. (Joint with H. Shin)

We gave a new construction of sequences of pseudo-Anosov braids with small normalized entropies. As an application, we proved that the minimal entropy among pseudo-Anosov elements in the spin mapping class group of genus g behaves like 1/g. Moreover the minimal entropy among pseudo-Anosov skew-palindromic braids with n strands behaves like 1/n. (Joint with S. Hirose)

Free Research Field

位相幾何学