Algebraic Topology


The course will give an introduction to algebraic topology with a focus on homotopy theory. Here is a more detailed syllabus:

Text:

  • M. Hovey: Model Categories, Mathematical Surveys and Monographs, vol. 63, Amer. Math. Soc.
  • D. G. Quillen: Homotopical Algebra, Lecture Notes in Mathematics, vol. 43, Springer-Verlag, New-York.
  • S. Schwede: An Untitled Book Project about Symmetric Spectra. Available for free download here.
  • Time and place:

    Lecture 1: Thursday, April 12, 1:00-2:30 in 309. Note: The Topologist's Sine Curve.

    Lecture 2: Tuesday, April 17, 1:00-2:30 in 309. Note: The model category axioms.

    Lecture 3: Thursday, April 19, 1:00-2:30 in 309. Note: The right and left homotopy relations.

    Lecture 4: Tuesday, May 8, 3:00-4:30 in 309. Problem set 1 is due.

    Lecture 5: Thursday, May 10, 1:00-2:30 in 309. Note: Cofibrantly generated model categories

    Lecture 6: Tuesday, May 15, 3:00-4:30 in 309.

    Lecture 7: Thursday, May 17, 1:00-2:30 in 309.

    Lecture 8: Tuesday, May 29, 2:45-4:15 in 309. Problem set 2 is due.

    Lecture 9: Thursday, May 31, 1:00-2:30 in 309.

    Lecture 10: Tuesday, June 12, 3:00-4:30 in 309.

    Lecture 11: Thursday, June 14, 1:00-2:30 in 309.

    Lecture 12: Tuesday, June 26, 3:00-4:30 in 309.

    Lecture 13: Thursday, June 28, 1:00-2:30 in 309.

    Lecture 14: Tuesday, July 10, 3:00-4:30 in 309.

    Lecture 15: Thursday, July 12, 1:00-2:30 in 309.