### Abstract

After fixing a marking (V,W) of a quasi-Fuchsian punctured torus group G, the complex lengthλV and the complex twist tV,W parameters define a holomorphic embedding of the quasi-Fuchsian space QF of punctured tori into C2. It is called the complex Fenchel-Nielsen coordinates of QF. For c ∈ C, let Q ^{γ,c} be the affine subspace of C2 defined by the linear equationλV = c. Then we can consider the linear slice Lc of QF by QF n Q ^{γ,c} which is a holomorphic slice of QF. For any positive real value c, Lc always contains the so-called Bers-Maskit slice BM ^{γ,c} defined in [Topology 43 (2004), no. 2, 447-491]. In this paper we show that if c is sufficiently small, then Lc coincides with BM ^{γ,c} whereas Lc has other components besides BM ^{γ,c} when c is sufficiently large. We also observe the scaling property of Lc.

Original language | English |
---|---|

Pages (from-to) | 89-102 |

Number of pages | 14 |

Journal | Conformal Geometry and Dynamics |

Volume | 16 |

DOIs | |

Publication status | Published - 2012 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Conformal Geometry and Dynamics*,

*16*, 89-102. https://doi.org/10.1090/S1088-4173-2012-00237-8

**Linear slices of the quasi-fuchsian space of punctured tori.** / Komori, Yohei; Yamashita, Yasushi.

Research output: Contribution to journal › Article

*Conformal Geometry and Dynamics*, vol. 16, pp. 89-102. https://doi.org/10.1090/S1088-4173-2012-00237-8

}

TY - JOUR

T1 - Linear slices of the quasi-fuchsian space of punctured tori

AU - Komori, Yohei

AU - Yamashita, Yasushi

PY - 2012

Y1 - 2012

N2 - After fixing a marking (V,W) of a quasi-Fuchsian punctured torus group G, the complex lengthλV and the complex twist tV,W parameters define a holomorphic embedding of the quasi-Fuchsian space QF of punctured tori into C2. It is called the complex Fenchel-Nielsen coordinates of QF. For c ∈ C, let Q γ,c be the affine subspace of C2 defined by the linear equationλV = c. Then we can consider the linear slice Lc of QF by QF n Q γ,c which is a holomorphic slice of QF. For any positive real value c, Lc always contains the so-called Bers-Maskit slice BM γ,c defined in [Topology 43 (2004), no. 2, 447-491]. In this paper we show that if c is sufficiently small, then Lc coincides with BM γ,c whereas Lc has other components besides BM γ,c when c is sufficiently large. We also observe the scaling property of Lc.

AB - After fixing a marking (V,W) of a quasi-Fuchsian punctured torus group G, the complex lengthλV and the complex twist tV,W parameters define a holomorphic embedding of the quasi-Fuchsian space QF of punctured tori into C2. It is called the complex Fenchel-Nielsen coordinates of QF. For c ∈ C, let Q γ,c be the affine subspace of C2 defined by the linear equationλV = c. Then we can consider the linear slice Lc of QF by QF n Q γ,c which is a holomorphic slice of QF. For any positive real value c, Lc always contains the so-called Bers-Maskit slice BM γ,c defined in [Topology 43 (2004), no. 2, 447-491]. In this paper we show that if c is sufficiently small, then Lc coincides with BM γ,c whereas Lc has other components besides BM γ,c when c is sufficiently large. We also observe the scaling property of Lc.

UR - http://www.scopus.com/inward/record.url?scp=84865088169&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865088169&partnerID=8YFLogxK

U2 - 10.1090/S1088-4173-2012-00237-8

DO - 10.1090/S1088-4173-2012-00237-8

M3 - Article

VL - 16

SP - 89

EP - 102

JO - Conformal Geometry and Dynamics

JF - Conformal Geometry and Dynamics

SN - 1088-4173

ER -