math 544: topology
jump to current week
math544.zulipchat.com
- Instructor: Kyle Ormsby
- TA: Alex Waugh
- Text: Introduction to Topological Manifolds (2nd ed.) by Lee
- Course Information & Syllabus
- Problem session: Tuesdays 13:00-14:00 in the graduate lounge
- Drop-in hours: W 12:30–13:30 with Alex in C-132, Th 15:00–16:00 (and by appointment) with Kyle in C-442
Students are strongly encouraged to typeset their work in $\LaTeX$. You can get started easily with Overleaf. To facilitate your typesetting, for (nearly) all URL’s on this site ending in .pdf, you can change the suffix to .tex to access the source code.
week 1
28 September - 30 September
Wednesday: Welcome, warmup, and course policies
Friday: Topological spaces
- Reading: pp.19-37
- Supplemental reading: pp.1-17
- Notes, Recording
- Homework due: Welcome survey
week 2
3 October - 7 October
Monday: Manifolds
Wednesday: Subspaces, products
Friday: Quotients
week 3
10 October - 14 October
Monday: More quotients, gluing, group actions
Wednesday: Connectedness
Friday: Compactness
week 4
17 October - 21 October
Monday: Local and paracompactness
Wednesday: Partitions of unity and proper maps
Friday: Cell and CW complexes
week 5
24 October - 28 October
Monday: One-dimensional manifolds
Wednesday: Surfaces via polygons
Friday: Surface classification
week 6
31 October - 4 November
Monday: Euler characteristic & orientability
Wednesday: Homotopy & the fundamental group $\pi_1$
Friday: More on $\pi_1$
week 7
7 November - 11 November
Monday: Homotopy equivalence
Wednesday: Higher homotopy groups, categories & functors
Friday: Veterans Day, no class
- Homework due: week07
week 8
14 November - 18 November
Monday: Lifting properties of the circle
Wednesday: $\pi_1(S^1)\cong \mathbb{Z}$
Friday: Free products, free groups, & group presentations
week 9
21 November - 25 November
Monday: Seifert-van Kampen Theorem: statement & applications
Wednesday: Thanksgiving holiday, no class
Friday: Thanksgiving holiday, no class
week 10
28 November - 2 December
Monday: $\pi_1$ of compact surfaces & classification
Wednesday: Proof of Seifert-van Kampen
Friday: Knot groups
week 11
5 December - 9 December
Monday: Review & moduli of pentagons
Wednesday: Review & exponential topologies
Friday: Review, configuration spaces, & braids
finals week
12 December - 16 December
Thirty-minute oral exams. Scheduling link available on Zulip.