Appendix A: List of Symbols
- Page ID
- 80009
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Symbol | Description | Location |
---|---|---|
\(\mathbb{C}\) | the complex plane | Section 2.1 |
\(\mathbb{S}^1\) | the unit circle | Example 3.2.1 |
\(i_C(z)\) | inversion in the circle \(C\) | Section 3.2 |
\(\infty\) | the point at \(\infty\) | Section 3.3 |
\(\mathbb{C}^+\) | the etended complex plane | Section 3.3 |
\((\mathbb{C},{\cal T})\) | translational geometry | Example 4.1.4 |
\((\mathbb{C},{\cal E})\) | Euclidean geometry | Example 4.1.5 |
\((\mathbb{C}^+,{\cal M})\) | Möbius geometry | Definition of Möbius Geometry (Section 4.2) |
\((\mathbb{D},{\cal H})\) | the Poincaré disk model for hyperbolic geometry | Definition of Poincaré disk model for hyperbolic geometry (Section 5.1) |
\(\mathbb{D}\) | the hyperbolic plane | Definition of Poincaré disk model for hyperbolic geometry (Section 5.1) |
\(\mathbb{S}^1_\infty\) | the circle at \(\infty\) in \((\mathbb{D},{\cal H})\) | Section 5.1 |
\(\mathbb{P}^2\) | the projective plane | Definition of Projective Plane (Section 6.2) |
\((\mathbb{P}^2,{\cal S})\) | the disk model for elliptic geometry | Definition of Disk Model for Elliptic Geometry (Section 6.2) |
\((\mathbb{P}^2_k,{\cal S}_k)\) | the disk model for elliptic geometry with curvature \(k\) | 0" href="/Bookshelves/Geometry/Geometry_with_an_Introduction_to_Cosmic_Topology_(Hitchman)/07:_Geometry_on_Surfaces/7.02:_Elliptic_Geometry_with_Curvature__k__0">Section 7.2 |
\((\mathbb{D}_k,{\cal H}_k)\) | the disk model for hyperbolic geometry with curvature \(k\) | Section 7.3 |
\((X_k,G_k)\) | \(2\)-dimensional geometry with constant curvature \(k\) | Definition of Geometry \((X_k, G_k)\) (Section 7.4) |
\(\mathbb{R}^n\) | real \(n\)-dimensional space | Section 7.5 |
\(X_1 \# X_2\) | the connected sum of two surfaces | Section 7.5 |
\(\mathbb{T}^2\) | the torus | Example 7.5.3 |
\(H_g\) | the handlebody surface of genus \(g\) | Section 7.5 |
\(C_g\) | the cross-cap surface of genus \(g\) | Section 7.5 |
\(\mathbb{K}^2\) | the Klein bottle | Example 7.5.4 |
\(\chi(S)\) | the Euler characteristic of a surface | Definition of Euler Characteristic (Section 7.5) |
\(X/G\) | the quotient set built from geometry \((X,G)\) | Section 7.7 |
\(\mathbb{H}^3\) | hyperbolic \(3\)-space | Section 8.1 |
\(\mathbb{S}^3\) | the \(3\)-sphere | Section 8.1 |
\(\mathbb{T}^3\) | the \(3\)-torus | Example 8.1.1 |