MATH 8302: Manifolds and Topology II (Spring 2018) |

Lecturer: Craig Westerland, 459 Vincent Hall, 612-625-0523, cwesterl@umn.edu.

Lecture: 1:25 -- 2:15 Monday, Wednesday, Friday, Vincent Hall 207.

Office Hours: 11:20 -- 1:20 Friday.

This is the second semester of a yearlong sequence in algebraic and differential topology. The main topics include basic homology and cohomology, vector fields and their Lie brackets, differential forms, deRham cohomology, Stokes' theorem, embeddings and immersions, submersions and fibre bundles, intersection theory and transversality. Students are assumed to have passed the previous semester of the course.

There is no official textbook for the course; however, the following are excellent references:

- Allen Hatcher, Algebraic Topology.
- William Massey, Algebraic Topology: an introduction.
- John Milnor, Topology from the Differentiable Viewpoint.
- Victor Guillemin and Alan Pollack, Differential Topology.

Massey's text is an excellent reference for the classification of surfaces, the fundamental group, and the classification of covering spaces. Hatcher's text is now a standard reference for most basic algebraic topology. Milnor's and Guillemin-Pollack's texts will be more useful in the second semester of the course.

Additionally, this is a series of lectures by John Milnor on differential topology. In addition to being an excellent resource on mathematics, it's evidence that there was a time when mathematicians wore suits, apparently.

Will consist of weekly homework (65%) and a take-home final (35%). The homework will be posted here:

- Homework 1, due Monday 12 February.
- Homework 2, due Monday 26 February.
- Homework 3, due Monday 26 March.
- Homework 4, due Friday 13 April.

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