2014/12/29 by Yuichi Kabaya, Kabaya, Yuichi
Mathematics · #20H10 #22E40 #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:20H10 #msc:22E40 #msc:57M50
paper · pdf · doi:10.48550/arxiv.1412.8441
19 pages, 2 figures. v3: minor changes, v2: pictures added in a new section
openalex publication_date 2014/12/29 · arxiv created 2022/03/14 · arxiv updated 2022/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The linear slice of quasi-Fuchsian once-punctured torus groups is defined by fixing the complex length of some simple closed curve to be a fixed positive real number. It is known that the linear slice is a union of disks, and it always has one standard component containing Fuchsian groups. Komori and Yamashita proved that there exist non-standard components if the length is sufficiently large. We give two other proofs of their theorem, one is based on some properties of length functions, and the other is based on the theory of complex projective structures and complex earthquakes. From the latter proof, we can characterize the existence of non-standard components in terms of exotic projective structures with quasi-Fuchsian holonomy.