The boundary of a fibered face of the magic 3-manifold and the asymptotic behavior of the minimal pseudo-Anosovs dilatations

2012/05/14 by Eiko Kin, Kin, Eiko, Mitsuhiko Takasawa +1
Computer Science · Mathematics · #37B40 #37E30 #57M27 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.DS #math.GT #msc:37B40 #msc:37E30 #msc:57M27

paper · pdf · doi:10.48550/arxiv.1205.2956

13 pages, 1 figures

openalex publication_date 2012/05/14 · arxiv created 2013/10/23 · arxiv updated 2013/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let δ_g,n be the minimal dilatation of pseudo-Anosovs defined on an orientable surface of genus g with n punctures. Tsai proved that for any fixed g ≥ 2, the logarithm of the minimal dilatation log δ_g,n is on the order of (log n)/(n). The main result of this paper is that if 2g+1 is relatively prime to s or s+1 for each 0 ≤ s ≤ g, then \limsup_{n → ∞} \fracn log δ_g,nlog n ≤ 2.

Citations

• Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle

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