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 $\mu\colon|K'|\to|K|$ |