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.

- Deadline 2/8, 10 am: Homework for lectures 1-4.
- Deadline 2/27, 10 am: Homework for lectures 4-8.