### 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 |
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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