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.
  • A. Hatcher: Algebraic Topology, Cambridge University Press. Available for free download here.
  • D. G. Quillen: Homotopical Algebra, Lecture Notes in Mathematics, vol. 43, Springer-Verlag, New-York.

    • Time and place:

    Lecture 1: Thursday, April 13, 1:00-2:30 in 453. Summary. Note: The Topologist's Sine Curve.

    Lecture 2: Tuesday, April 18, 2:30-4:00 in 455. Summary. Note: The model category axioms.

    Lecture 3: Thursday, April 20, 1:00-2:30 in 453. Summary. Note: The right and left homotopy relations.

    Lecture 4: Tuesday, April 25, 2:30-4:00 in 455. Summary.

    Lecture 5: Thursday, May 11, 1:00-2:30 in 453. Summary.

    Lecture 6: Tuesday, May 16, 2:30-4:00 in 455. Summary. Note: Limits and colimits.

    Lecture 7: Thursday, May 18, 1:00-2:30 in 453. Summary. Note: Cofibrantly generated model categories.

    Lecture 8: Tuesday, May 23, 2:30-4:00 in 455. Summary.

    Lecture 9: Thursday, May 25, 1:00-2:30 in 453. Summary.

    Lecture 10: Tuesday, June 13, 2:30-4:00 in 455. Summary.

    Lecture 11: Thursday, June 15, 1:00-2:30 in 453. Summary.

    Lecture 12: Tuesday, June 27, 2:30-4:00 in 455. Summary.

    Lecture 13: Thursday, June 29, 1:00-2:30 in 453. Summary.

    Lecture 14: Tuesday, July 11, 2:30-4:00 in 453.

    Lecture 15: Thursday, July 13, 1:00-2:30 in 453.