1. Introduction (12/10/2020).
  2. Paths and Homotopies (19/10/2020).
  3. Path and Homotopy Lifting (26/10/2020).
  4. Functoriality and Applications (2/11/2020).
  5. Free Groups (9/11/2020).
  6. Map Lifting and Classification of Covers (16/11/2020).
  7. Galois Theory of Covering Spaces (23/11/2020).
  8. Free Products and the Seifert-Van Kampen theorem (7/12/2020).
  9. Graphs and Two-Complexes (14/12/2020).
  10. CW-Complexes and Higher Homotopy Groups (21/12/2020).
  11. Whitehead Theory (28/12/2020).
  12. Simplicial Complexes and Homology (11/1/2021).

Introduction

due by Monday, Oct 12, 2020

  1. Prove or disprove in each case that the lifting problem has a solution.

  2. Prove or disprove each statement concerning the following commutative diagram with $X$ and $Y$ given topological spaces, $g$ a given continuous function and where we seek a solution for $f$ that is continuous.

    • a. If $g$ is injective the diagram has a solution.
    • b. If $g$ is surjective the diagram has a solution.
    • c. If the diagram has a solution then $g$ is injective.
    • d. If the diagram has a solution then $g$ is surjective.