Differentiable Manifolds II
Math 519, Spring 2013

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Course details       Grading scheme       Suggested Problems

Course Details

Lectures: TR 11:00-12:20, 445 Altgeld Hall

Instructor: Ely Kerman, ekerman@math.uiuc.edu

Office & Telephone: Illini Hall 326, 265-6710

Office Hours: By appointment. I am usually available T and Th from 12:45 to 1:45. I am also available on some W's. Please email me to arrange a time.

Course Description. This semester we will cover the following four topics: (1) de Rham cohomology (chapters 15 and 16 of Lee's text) (2) Intersection theory (Guillemin and Pollack), (3) Morse theory, (4) Introductory Riemannian geometry (Morse theory of geodesics following Milnor's text and Bishop's notes (see below)).

Geometry Notes. Professor Richard Bishop has generously given us open access to his Lecture Notes on Riemannian Geometry. We will use these notes as a primary source in the fourth section of the course.

Grading Scheme

The course grade will be based on class participation. I will pose exercises in lecture and will list some suggested problems from various sourcea throughout the semester. Please feel free to discuss these problems and/or your solutions with me at any time.

Suggested Problems (beyond the exercises mentioned in class)

  • From Lee's text
    15-1, 15-4, 15-5, 16-1, 16-2, 16-7.