Math 703, Theory of Manifolds I

Fall 2009

Instructor: Eduardo Cattani
Time and Place: Mo. - We. 2:30 - 3:45 in LGRT 1322
Textbook : None required. Several books are recommended; see reserve list below.
E-mail: Use: my lastname at math dot umass dot edu
Office: Lederle GRT 1235E
Office Hours:
- Monday: 4:15 to 5:15
- Wednesday: 11:30 to 12:30
- Thursday: 2:30 - 3:30

Course Description

An introduction to the basic concepts of Differential Geometry, Differential Topology and Lie Theory. Topics include: A review of differential maps between Euclidean spaces, Inverse and Implicit Function Theorems. Differentiable manifolds, definition and examples. Regular and critical values, Sard''s Theorem. submanifolds, immersions and embeddings. Vector bundles, tangent and cotangent bundles. Vector fields, ODE''s on manifolds, Lie bracket, integrable distributions, Frobenius Theorem. Differential forms, exterior differential.

Course Structure and Grading Policies:

There will be regular homework assignments. Some of the problems will be graded. No late homework will be accepted. You are encouraged to discuss the problems with your classmates but each student should write up his or her own solutions.
There will be a midterm and a final exam. The final exam will be comprehensive but will emphasize the material not covered in the midterm.
Your homework scores and class participation will count for 30% of the grade. The midterm score will count for 30% of the grade and the final exam score will count for the remaining 40% of the grade.

Bibliography:

The following books will be in Library Reserve:

CallNumber	Author	Title
QA613 .L44 2003	John Lee	Intro. to Smooth Manifolds
QA614.3 .B6 1986	William Boothby	An introduction to differentiable manifolds and Riemannian geometry.
QA614.3 .W37 1983	Frank Warner	Foundations of differentiable manifolds and Lie groups
QA641 .S59 1979	Michael Spivak	A comprehensive introduction to differential geometry
QA613.6 .G84	V. Guillemin and A. Pollack	Differential topology

Homework Assignments:

Assignments are due on the indicated date.

Math 703, Theory of Manifolds I

Fall 2009

Course Description

Course Structure and Grading Policies:

Bibliography:

Homework Assignments:

Problem Set #1

Problem Set #2

Problem Set #3

Problem Set #4

Problem Set #5

Exam Schedule: