紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2019, 56(2), p. 213-227

A CLASSIFICATION PROBLEM ON MAPPING CLASSES ON FIBER SPACES OVER TEICHMÜLLER SPACES

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2019-04

Let S˜ be an analytically finite Riemann surface which is equipped with a hyperbolic metric. Let S = S˜{one point x}. There exists a natural projection Π of the x-pointed mapping class group ModxS onto the mapping class group Mod(S˜). In this paper, we classify elements in the fiber Π−1(χ) for an elliptic element χ ∈ Mod(S˜), and give a geometric interpretation for each element in Π−1(χ). We also prove that Π−1(tna◦ χ) or Π−1(tna◦ χ−1) consists of hyperbolic mapping classes provided that tna◦ χ and tna◦ χ−1 are hyperbolic, where a is a simple closed geodesic on S˜ and ta is the positive Dehn twist along a.

10.18910/72314

72314

A CLASSIFICATION PROBLEM ON MAPPING CLASSES ON FIBER SPACES OVER TEICHMÜLLER SPACES

Osaka University and Osaka City University, Departments of Mathematics

英語

2019-04

Osaka Journal of Mathematics

56

2

213

227

https://hdl.handle.net/11094/72314

10.18910/72314

https://doi.org/10.18910/72314