About the study
The group reviewed Strom’s first chapter in May 2021 and restarted the reading in August alongside differential topology and measure theory.
Study plan
- Category theory: categories, functors, duality, groups and cogroups, limits and colimits, pushouts and pullbacks, and pointed spaces.
- Essential homotopy theory: the homotopy category, fibrations and cofibrations, homotopy limits and colimits, fiber and cofiber sequences, group actions, and CW-related constructions.
- Advanced homotopy theory: further study of fibrations, Hopf invariants, and infinite symmetric products.
- Algebraic topology: homology and cohomology, chain complexes, spectral sequences, and Bott periodicity.
- Optional additional topics: rational homotopy theory and Miller’s theorem.
Meeting format
- Saturday lectures at 4 p.m. EST, discussion on Discord/Element and a private question-and-answer workspace, and collaborative notes on Fandom.
- The syllabus included weekly reading and exercises, chapter quizzes, and longer tests.
Progress & milestones
- August 14: proposed 17–20 pages per week, covering the first 27 chapters.
- August 21: reviewed Chapter 1, pages 1–18, including categories, functors, and natural transformations.
- August 28: reduced the target to approximately 10–12 pages per week.
Background
Familiarity with groups, rings, and introductory topology.