| Symbol |
Description |
Location |
| \(\mathbb{C}\) |
the complex plane |
Paragraph |
| \(\mathbb{S}^1\) |
the unit circle |
Example 3.2.1 |
| \(i_C(z)\) |
inversion in the circle \(C\) |
Paragraph |
| \(\infty\) |
the point at \(\infty\) |
Paragraph |
| \(\mathbb{C}^+\) |
the etended complex plane |
Paragraph |
| \((\mathbb{C},{\cal T})\) |
translational geometry |
Example 4.1.6 |
| \((\mathbb{C},{\cal E})\) |
Euclidean geometry |
Example 4.1.11 |
| \((\mathbb{C}^+,{\cal M})\) |
Möbius geometry |
Definition 4.2.1 |
| \((\mathbb{D},{\cal H})\) |
the Poincaré disk model for hyperbolic geometry |
Definition 5.1.1 |
| \(\mathbb{D}\) |
the hyperbolic plane |
Definition 5.1.1 |
| \(\mathbb{S}^1_\infty\) |
the circle at \(\infty\) in \((\mathbb{D},{\cal H})\) |
Paragraph |
| \(\mathbb{P}^2\) |
the projective plane |
Definition 6.2.6 |
| \((\mathbb{P}^2,{\cal S})\) |
the disk model for elliptic geometry |
Definition 6.2.8 |
| \((\mathbb{P}^2_k,{\cal S}_k)\) |
the disk model for elliptic geometry with curvature \(k\) |
Paragraph |
| \((\mathbb{D}_k,{\cal H}_k)\) |
the disk model for hyperbolic geometry with curvature \(k\) |
Paragraph |
| \((X_k,G_k)\) |
2-dimensional geometry with constant curvature \(k\) |
Definition 7.4.1 |
| \(\mathbb{R}^n\) |
real \(n\)-dimensional space |
Paragraph |
| \(X_1 \# X_2\) |
the connected sum of two surfaces |
Paragraphs |
| \(\mathbb{T}^2\) |
the torus |
Example 7.5.9 |
| \(H_g\) |
the handlebody surface of genus \(g\) |
Paragraph |
| \(C_g\) |
the cross-cap surface of genus \(g\) |
Paragraph |
| \(\mathbb{K}^2\) |
the Klein bottle |
Example 7.5.15 |
| \(\chi(S)\) |
the Euler characteristic of a surface |
Definition 7.5.22 |
| \(X/G\) |
the quotient set built from geometry \((X,G)\) |
Paragraph |
| \(\mathbb{H}^3\) |
hyperbolic 3-space |
Paragraphs |
| \(\mathbb{S}^3\) |
the 3-sphere |
Paragraphs |
| \(\mathbb{T}^3\) |
the 3-torus |
Example 8.1.2 |
