LINEAR SLICES OF THE QUASI-FUCHSIAN SPACE OF PUNCTURED TORI.

After fixing a marking (V,W) of a quasi-Fuchsian punctured torus group G, the complex length λ_V and the complex twist τ_V,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 equation λ_V = 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 Lc has other components besides BM_{γ ,c} when c is sufficiently large. We also observe the scaling property of L_c. [ABSTRACT FROM AUTHOR]