Linear slices of the quasifuchsian space of punctured tori
Abstract
After fixing a marking (V, W) of a quasifuchsian punctured torus group G, the complex length lV and the complex twist tauV,W parameters define a holomorphic embedding of the quasifuchsian space QF of punctured tori into C2. It is called the complex Fenchel-Nielsen coordinates of QF. For a complex number c, let Qgamma,c be the affine subspace of C2 defined by the linear equation lV=c. Then we can consider the linear slice L of QF by QF Qgamma,c which is a holomorphic slice of QF. For any positive real value c, L always contains the so called Bers-Maskit slice BMgamma,c. In this paper we show that if c is sufficiently small, then L coincides with BMgamma,c whereas L has other components besides BMgamma,c when c is sufficiently large. We also observe the scaling property of L.