Math 432/532 WINTER 2019, List of lectures

  • On this page I will post content of all lectures. All handouts also will be posted here.
  • Monday, January 7: Definition of manifold. Section 1.1. Please find your homework.
  • Wednesday, January 9: Examples of manifolds. Section 1.1.
  • Friday, January 11: Chain Rule. Section 1.2.
  • Monday, January 14: Tangent spaces. Section 1.2. New homework.
  • Wednesday, January 16: Tangent map. Local diffeomorphisms. Sections 1.2-1.3.
  • Friday, January 18: Immersions. Section 1.3. New homework.
  • Monday, January 21: no classes, Martin Luther King Jr holiday.
  • Wednesday, January 23: Embeddings vs Immersions. Section 1.3.
  • Friday, January 25: Submersions. Section 1.4. New homework.
  • Monday, January 28: Regular values and examples of manifolds. Section 1.4.
  • Wednesday, January 30: Transversality. Section 1.5.
  • Friday, February 1: Properties stable under deformations. Section 1.6. New homework.
  • Monday, February 4: Stable classes of maps. Section 1.6.
  • Wednesday, February 6: Sard's theorem. Section 1.7.
  • Friday, February 8: Morse functions. Section 1.7. We will have MIDTERM next Friday!!! There will be NO homework due next Friday.
  • Monday, February 11: Whitney's embedding theorem for compact manifolds. Section 1.8.
  • Wednesday, February 13: Whitney's embedding theorem in general. Section 1.8.
  • Friday, February 15: MIDTERM. New homework.
  • Monday, February 18: More on Whitney's embedding theorem. Boundaries. Sections 1.8 and 2.1.
  • Wednesday, February 20: Theorems on manifolds with boundaries. Section 2.1.
  • Friday, February 22: Pre-images for maps of manifolds with boundaries. Section 2.1. New homework.
  • Monday, February 25: No classes because of snow.
  • Wednesday, February 27: No classes because of snow.
  • Friday, March 1: Classification of 1-manifolds and Brouwer's fixed point theorem. Section 2.2.
  • Monday, March 4: More on transversality. Section 2.3. New homework.
  • Wednesday, March 6: Intersection theory mod 2. Section 2.4.
  • Friday, March 8: More of intersection theory. Section 2.4.
  • Monday, March 11: The Jordan-Brouwer Separation Theorem. Section 2.5. Please find practice problems for the final!
  • Wednesday, March 13: The Borsuk-Ulam Theorem. Section 2.6.
  • Friday, March 15: Review.
  • END