Bers embedding of the Teichmüller space of a once-punctured torus

Abstract

Abstract. In this note, we present a method of computing monodromies of projective structures on a once-punctured torus. This leads to an algorithm numerically visualizing the shape of the Bers embedding of a one-dimensional Teichmüller space. As a by-product, the value of the accessory parameter of a four-times punctured sphere will be calculated in a numerical way as well as the generators of a Fuchsian group uniformizing it. Finally, we observe the relation between the Schwarzian differential equation and Heun's differential equation in this special case.

The automorphism groups of the profinite braid groups

“…Proof of Proposition 3.2 (i): Let us begin with geometric interpretation of Π 0,4 ⊂ ker(b 43 ) which has been well studied by topologists (see, e.g., [ASWY,§2.1], [KS,§3]). One may regard the standard lift…”

On dynamics of Out(F_n) on PSL(2,C) characters

“…For rank n = 2, the character variety has complex dimension 2, and one can try to draw slices of dimension 1. Komori-Sugawa-Wada-Yamashita developed a program for drawing Bers slices, which are parts of the discrete faithful locus [31,30], and Dumas refined this using Bowditch's work [16]. In particular what Dumas' program is really doing is drawing slices of Bowditch's domain BQ.…”