math 546: manifolds
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math544.zulipchat.com
- Instructor: Kyle Ormsby
- TA: Alex Waugh
- Text: Introduction to Smooth Manifolds
- Course Information & Syllabus
- Problem session: Tu 13:30-14:20 in THO 217
- Drop-in hours: W 12:30-13:30 with Alex in C-132, Th 15-16 (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
27 March - 31 March
Monday: Welcome & warmup
Wednesday: Lie groups
Friday: Group actions and equivariance
week 2
3 April - 7 April
Monday: Vector fields
Wednesday: Lie brackets
Friday: Lie algebras
week 3
10 April - 14 April
Monday: Integral curves and flows
Wednesday: Lie derivatives
Friday: Vector bundles
week 4
17 April - 21 April
Monday: More vector bundles
Wednesday: Cotangent bundle
Friday: Line integrals and conservative covector fields
week 5
24 April - 28 April
Monday: Tensors
Wednesday: Tensor fields
Friday: Differential forms
week 6
1 May - 5 May
Monday: Orientations
Wednesday: Orientations and covering maps
Friday: Integration of differential forms
week 7
8 May - 12 May
Monday: Stokes’ theorem
Wednesday: de Rham cohomology
Friday: Homotopy invariance and Mayer-Vietoris
week 8
15 May - 19 May
Monday: Degree theory
Wednesday: Singular cohomology
Friday: The de Rham theorem
week 9
22 May - 26 May
Monday: Riemannian manifolds
Wednesday: The tangent-cotangent isomorphism
- Reading: pp.337-343
Friday: Quotient manifolds
week 10
29 May - 2 June
Monday: Memorial Day, no class
Wednesday: Review
Friday: Review
- Recording
- Homework due: none.
finals week
5 June - 9 June
- See Zulip for sign-up link.
- Practice problems