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

Lecture: 1:25 -- 2:15 Monday, Wednesday, Friday, Vincent Hall 206.

Office Hours: 2:15 -- 3:45 Monday, 9:30 -- 11 Thursday.

Goals and Objectives

This is the first semester of a yearlong sequence in algebraic and differential topology. The main topics include compact surfaces, the fundamental group, and basic homology and cohomology. Students are assumed to have command of point-set topology and basic algebra. The focus of this semester will be much more on the algebraic topology side of the subject, and next semester on differential topology.

References

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.

Assessment

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

• Homework 1, due Monday 11 September.
• Homework 2, due Monday 18 September.
• Homework 3, due Monday 25 September.
• Homework 4, due Monday 2 October.
• Homework 5, due Monday 9 October.
• Homework 6, due Monday 23 October.
• Homework 7, due Monday 30 October.
• Homework 8, due Monday 6 November.
• Homework 9, due Wednesday 15 November.
• Homework 10, due Wednesday 22 November.
• Homework 11, due Wednesday 6 December.