# 547 - Algebraic Topology 1 - Fall 2019 - UIC

Back.

**Time:** `1400-1450 MWF.`

**Place:** `Taft Hall 305.`

**E-mail:** `benjamin.antieau@gmail.com`.

**Course webpage:** `dantie1.people.uic.edu/201801-547.html`

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**Office hours:** 1200-1250 MF in `SEO 419`.

**Book:** I will use Hatcher's *Algebraic Topology* in general and Fulton's *Algebraic Topology: A First Course* for the proof of van Kampen's theorem.

**Syllabus** (detailed outline):
- Wk 1: homotopy theory and categories.
- Wk 2: the fundamental group.
- Wk 3: covering spaces.
- Wk 4: more covering spaces.
- Wk 5: proof of van Kampen.
- Wk 6: homological algebra.
- Wk 7: simplicial sets, homology, universal coefficients (no class 2/23).
- Wk 8: properties of homology; the Künneth isomorphism (no class 2/26).
- Wk 9: CW homology.
- Wk 10: cohomology, universal coefficients, properties.
- Wk 11: cup product.
- Wk 12: orientations
- Wk 13: Poincaré duality (no class 4/11).
- Wk 14: cohomology with compact supports and Poincar\'e duality.
- Wk 15: prelim prep.

**Reading:** all references are to Hatcher's book unless specified otherwise. This schedule is tentative.
- 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 and you must list your collaborators.

**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!