# Interactive pages for Algebraic Topology

 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 3.8 Finite element model Remark 2.3 A cylinder is homeomorphic to an annulus Example 4.7 Stereographic projection Example 4.10 $\mathbb{R}P^1$ is homeomorphic to $S^1$ Example 8.23
 Gluing two discs to make a sphere Example 8.24 Loops on the sphere Loops on the torus A homotopy of the trefoil Geometry of the Möbius strip Example 10.23 The Möbius strip and the circle Example 10.23 The punctured plane Example 10.23 The punctured sphere The punctured torus Remark 15.26 Wrapping an annulus Example 15.27 The exponential map The exponential map is a covering Proposition 12.6 Path lifting Proposition 12.9 Homotopy lifting Proposition 12.12 Boundary of a tetrahedron Example 18.7 Barycentric subdivision of a tetrahedron Example 22.5 The map $\mu\colon|K'|\to|K|$ Example 22.8