MATH 742 - Differential Topology

Objectives

We will study smooth manifolds. There is a great deal known about smooth manifolds, much more than can be covered in years of study, let alone a semester course. So the actual course content beyond the basics will be guided by the individual objectives of the students in the class. We will start with the basics, imbeddings, vector bundles, transversality, tubular neighborhoods. We'll then move on to other topics depending on class interest, for example, De Rham's theorem, elementary Morse theory and handlebody theory, singular spaces, and other topics.

I will write up what we did each day with appropriate references. Due to all the math the best way seems to be as a pdf file generated from TeX. If you would prefer some other format, let me know.

Text

We will not have an official text. References will be given and I will arrange for library books to be put on reserve if it would be useful. Some material is in

Bredon Topology and Geometry
Dubrovin, Fomenko, Novikov Modern Geometry- Methods and Applications, part II
Hirsch Differential Topology
Brocker and Janich Intrduction to Differential Topology
Milnor Topolgy from the Differentaible Viewpoint
Milnor Morse theory
Milnor Lectures on the h-cobordism Theorem
King Course Handouts

Factoring intervals from bundles

Watson here are writeups of Toni Watson's lectures

Instructor

Prof. Henry King
Office: 3111
Office Phone: (301) 405-5165.
E-mail: hking@math.umd.edu

Grading

There will be no exams. I do not plan to assign homework. However, I expect the students to be engaged in the class, for example giving talks, writing up some lectures, or researching some material outside the lectures, asking questions.