547 - Algebraic Topology 1 - Fall 2019 - UIC

• 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.

• 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.

• Due 09/06: HW 1.
• Due 09/13: HW 2.
• Due 09/20: HW 3.
• Due 09/30: HW 4.
• Due 10/07: HW 5.
• Due 10/25: HW 6.
• Due 11/4: HW 7.
• Due 11/15: HW 8.
• Due 12/6: HW 9.

• 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.

• 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!