### Abstract

After fixing a marking (V, W) of a quasi-Fuchsian punctured torus group G, the complex length λV and the complex twist τV, W parameters define a holomorphic embedding of the quasi-Fuchsian space QF of punctured tori into C^{2}. It is called the complex Fenchel-Nielsen coordinates of QF. For c ∈ C, let Q_{γ, c} be the affine subspace of C^{2} defined by the linear equation λV = c. Then we can consider the linear slice L_{c} of QF by QF ∩ Q_{γ, c} which is a holomorphic slice of QF. For any positive real value c, L_{c} 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 L_{c} coincides with BM_{γ, c} whereas L_{c} has other components besides BM_{γ, c} when c is sufficiently large. We also observe the scaling property of L_{c}.

Original language | English |
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Pages (from-to) | 89-102 |

Number of pages | 14 |

Journal | Conformal Geometry and Dynamics |

Volume | 16 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2012 Apr 4 |

Externally published | Yes |

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

*Conformal Geometry and Dynamics*,

*16*(5), 89-102. https://doi.org/10.1090/S1088-4173-2012-00237-8