547 - Algebraic Topology 1 - Spring 2018 - UIC
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Time: 1000-1050 MWF.
Place: Stevenson Hall 316.
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.
Syllabus (detailed outline):
- Wk 1: homotopy theory and categories.
- Wk 2: the fundamental group(oid) and the van Kampen theorem.
- Wk 3: covering spaces.
- Wk 3: more covering spaces and van Kampen.
- Wk 5: homological algebra.
- Wk 6: simplicial sets, homology, universal coefficients (no class 2/23).
- Wk 7: properties of homology; the Künneth isomorphism (no class 2/26).
- Wk 8: CW homology.
- Wk 9: cohomology, universal coefficients, properties.
- Wk 10: cup product.
- Wk 11: orientations
- Wk 12: Poincaré duality (no class 4/11).
- Wk 13: cohomology with compact supports and Poincar\'e duality.
- Wk 14: prelim prep.
- Wk 15: prelim prep.
Reading:
- Wk 1: Chapter 0.
- Wk 2: Section 1.1.
- Wk 3: Sections 1.2 and 1.3.
- Wk 4: Section 1.2 and 1.3.
- Wk 5: Chapter 1 of Weibel if possible. Read this excerpt for the details on G-coverings.
- Wk 6: Section 2.1.
- Wk 7: Section 2.2.
- Wk 8: Sections 2.2 and 2.3.
- Wk 9: Section 3.1.
- Wk 10: Section 3.2.
- Wk 11: Section 3.3, Orientations.
- Wk 12: Section 3.3, Poincar\'e duality.
- Wk 13: Section 3.3, Poincar\'e duality.
- Wks 14-15: Review.
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!