# 547 - Algebraic Topology 1 - Spring 2018 - UIC

Back.

**Time:** `1000-1050 MWF.`

**Place:** `Stevenson Hall 316.`

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

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

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**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:**
- 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.
- Wk 7: properties of homology; the Künneth isomorphism (no class 2/23).
- Wk 8: simplicial complexes (no class 2/26).
- Wk 9: CW homology.
- Wk 10: cohomology, universal coefficients, properties.
- Wk 11: cohomology with compact supports and cap product.
- Wk 12: orientations and Poincaré duality.
- Wk 13: the cup product.
- Wk 14: the Lefschetz fixed point theorem.
- Wk 15: group cohomology.

**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.

**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!