This is the website of Spring 2018's Math 231br: Advanced algebraic topology. Here is the course information:

  • The syllabus.
  • The details about the papers and topic suggestions can be found here.
  • The collected notes will be combined with those of the 2019 version of this course.

Lectures

Below appear the lecture notes and further references.

  • 1/23, Lecture 1: Introduction and a convenient category of spaces.
  • 1/25, Lecture 2: Homotopy groups.
  • 1/30, Lecture 3: Exact sequences of spaces.
  • 2/1, Lecture 4: Cofibrations and fibrations.
  • 2/6, Lecture 5: CW-complexes.
  • 2/8, Lecture 6: CW-approximation and homotopy excision.
  • 2/13, Lecture 7: Singular cohomology and generalized cohomology theories.
  • 2/15, Lecture 8: Brown representability and spectra.
  • 2/20, Lecture 9: The stable homotopy category.
  • 2/22, Lecture 10: The Atiyah-Hirzebruch spectral sequence.
  • 2/27, Lecture 11: The Atiyah-Hirzebruch-Serre spectral sequence.
  • 3/1, Lecture 12: The cohomological Atiyah-Hirzebruch-Serre spectral sequence.
  • 3/6, Lecture 13: Principal G-bundles and classifying spaces.
  • 3/8, Lecture 14: Classifying spaces continued.
  • 3/20, Lecture 15: Characteristic classes of vector bundles<.
  • 3/22, Lecture 16: Bordism groups.
  • 3/27, Lecture 17: The Pontryagin-Thom theorem.
  • 3/29, Lecture 18: Steenrod operations.
  • 4/3, Lecture 19: The Steenrod algebra.
  • 4/5, Lecture 20: Thom's theorem.
  • 4/9, Lecture 21: Quasifibrations.
  • 4/11, Lecture 22: Bott periodicity and topological K-theory.
  • 4/17, Lecture 23: The homotopy of the cobordism category.
  • 4/19, Lecture 24: The scanning map.
  • 4/24, Lecture 25: Overview and outlook.

Homework

Below appear the homeworks.

Math 231br Spring 2018