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