Various surfaces | Section 1 |
A cube with holes | |
Trefoil knot | Section 1 |
Folding a square to make a torus | |
The torus as a quotient of the plane | |
Letters of the alphabet | Section 1 |
Letters grouped by type | Section 1 |
Cage with two or three holes | Section 1 |
Simplices | Section 1 |
Barycentric coordinates | |
Different triangulations of the sphere | Section 1 |
The triangle and the square | Section 1 |
Skeleta of simplices | Section 1 |
Open sets | Definition 3.7 |
Finite element model | |
A cylinder is homeomorphic to an annulus | Example 4.9 |
Stereographic projection | Example 4.13 |
$\mathbb{R}P^1$ is homeomorphic to $S^1$ | Example 7.23 |
Gluing two discs to make a sphere | Example 7.24 |
Loops on the sphere | |
Loops on the torus | |
A homotopy of the trefoil | |
Geometry of the Möbius strip | Example 9.21 |
The Möbius strip and the circle | Example 9.21 |
The punctured plane | Example 9.21 |
The punctured sphere | |
The punctured torus | Proposition 20.5 |
Wrapping an annulus | |
The exponential map | |
The exponential map is a covering | Proposition 22.7 |
Path lifting | Proposition 22.10 |
Homotopy lifting | |
Subdivision of a prism $[0,1]\times\Delta_2$ | Section 18 |
Boundary of a tetrahedron | Example 10.13 |
Barycentric subdivision of a tetrahedron | Section 18 |
The map $\mu\colon|K'|\to|K|$ |