548 - Algebraic Topology 2 - Spring 2018 - UIC
Back.
Time: 1100-1150 MWF.
Place: Stevenson Hall 103.
E-mail: benjamin.antieau@gmail.com.
Course webpage: dantie1.people.uic.edu/201801-547.html.
Office hours: 1500-1600 MW in SEO 419.
Book: I will use Hatcher's book, Algebraic Topology, Switzer's Algebraic Topology, and May's A Concise Course in Algebraic Topology. We will also have occasion to use the article Homotopy theories and model categories by Dwyer and Spalinski.
Tentative Syllabus:
- Wk 1: the loops-suspension adjunction.
- Wk 2: higher homotopy groups.
- Wk 3: model categories.
- Wk 4: the homotopy category and the model categorical Whitehead's theorem.
- Wk 5: the model category structure on topological spaces.
- Wk 6: long exact sequences in higher homotopy groups (no class 2/23).
- Wk 7: Blakers-Massey after Rezk (no class 2/26).
- Wk 8: the theorem of Hurewicz, Eilenberg-MacLane spaces, and Postnikov towers.
- Wk 9: Eilenberg-MacLane spaces and spectra.
- Wk 10: vector bundles.
- Wk 11: Grassmannians and vector bundles.
- Wk 12: Leray-Hirsch I and chern classes.
- Wk 13: filtered chain complexes.
- Wk 14: the Serre spectral sequence.
- Wk 15: applications of spectral sequences.
Reading:
- Wk 1: Pages 393-396 from Hatcher as well as the compact-open topology section from the appendix.
- Wk 2: Pages 337 through Proposition 4.2.
- Wk 3: Sections 3 and 4 from Dwyer-Spalinski.
- Wk 4: Sections 5-6 and 8 from Dwyer and Spalinski.
- Wk 5: Section 8 from Dwyer and Spalinski.
- Wk 6: Section 4.1.
- Wk 7: Section 4.2.
- Wk 8: Material on Postnikov towers and the Hurewicz theorem from 4.1 and 4.2.
- Wk 9: Material on cohomology theories and spectra from 4.3.
- Wk 10: Material on Stiefel and Grassmannians from 4.2.
- Wk 12: 4D.
- Wk 13: more 4D.
- Wk 14: Chapter 5 of Weibel or the paper of Gwilliam–Pavlov entitled Enhancing the filtered derived category [arxiv].
- Wk 15: Chapter 5 and Section 6.1 of McCleary's book A user's guide to spectral sequences.
Homework:
Evaluation:
- The final grade will be based on completion of the homework. It will be typically be assigned each Friday and due the following Friday with no late assignments accepted.
- You are encouraged to work collectively on the homework, though your solution will be written up in your own words. You must cite any outside source you have used
in finding your solution.
Miscellanea:
- If you wish to request an accommodation due to a disability, please contact the Disability Resource Center at +1-312-413-2183.
- Come to office hours!