# Discreteness Locus

This section is based on the joint work with Y. Komori, T. Sugawa and M. Wada.
The following pictures are slices of the parameter space of once-punctured torus groups.

## 1. Bers slice

### 1-1. Base point = hexagonal torus.

### 1-2. Base point = square torus.

### 1-3. Other Bers slices

## 2. Earle slice

## 3. Maskit slice (Tr b = 2)

## 4. Linear slice (trace constant slice)

### 4-1. Tr b = 2 + 6i (see Figure 10.20 in Indra's Pearls)

### 4-2. Tr b = 1.91 + 0.05i (see Figure 10.19 in Indra's Pearls)

### 4-3. Other examples

# Convex hull boundary (pleated surface)

I am impressed by the nice picture of Figure 12.6 in "Indra's Pearls".
(The picture was produced by Yair Minsky.
See his limit set pictures.)
I wanted to draw these nice pictures.
Here are some of the pictures I produced.

### Tr a = 2.7, Tr b = 2.7

### Tr a = 2.5, Tr b = 2.5

### Tr a = 2.2, Tr b = 2.2

### Tr a = 2, Tr b = 2

### Tr a = 3, Tr b = 2+0.5i

### Tr a = 3, Tr b = 1.91+0.05i

### Tr a = 3.5, Tr b = 2.578456017+0.64347683583i

### Tr a = 2.03125, Tr b = 1.750069784+0.9998778635i

### Tr a = 4, Tr b = 2.071677342+0.761020644i

### Tr a = 10, Tr b = 2.683021785+0.558833926i

### Tr a = 64, Tr b = 4.862001682+0.6774259456i

Last update: Apr. 4, 2009