I am teaching a lecture series on "Manifolds". See here for the website of the program.

(Tentative) Overview of content

• Manifolds - an introduction via examples
• Surfaces from polygons and classification
• The fundamental group using polygons
• Tangent space and smooth manifolds

Some links with videos and extra materials

• Klein bottles:
  • How to make a Klein surface out of an old pair of jeans
  • Cutting a Klein bottle in half
• Surfaces from polygons Dance my PhD on double torus
• Moebius bagel
• A hole in a hole in a hole
• Torus games

Some links with lecture notes, freely available book, and other useful references

• Introduction to Differential Topology, Bjoern Dundas
• Algebraic Topology, Allen Hatcher
• Lectures on Surfaces: (Almost) Everything You Wanted to Know about Them, Anatole Katok and Vaughn Climenhaga
• Smooth Manifolds, John M. Lee
• Brain Conrad's handout on the Quotient Manifold Theorem
• Differential Forms in Algebraic Topology, Bott and Tu
• Topics in Morse Theory: Lecture Notes, Ralph Cohen, Iga, Norbury

Some exercises

Exercises

Miniprojects

Miniprojects