Theory of Manifolds, I

Last Problem Set

This is now in your mailbox.

Final exam

The final will be Saturday, 18 December, from 10:30-12:30. The exam will take place in LGRT 1114.

Instructor

Prof. Paul Gunnells, LGRT 1115L, 545-6009, gunnells at math dot umass dot edu.

Office Hours

Tuesdays and Thursdays, 8:30-9:30

Overview

Theory of manifolds I develops the basic topology and geometry of differentiable manifolds, including some basic Lie theory. Topics include 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.

Textbook

The required text is Boothby, "An Introduction to Differentiable Manifolds and Riemannian Geometry." Others that will be valuable are

These will be on reserve at the library.

Grading

There will be problem sets assigned during the term. Some problems will be graded, and will count for 25% of your grade. There will also be a midterm and a final exam, which will be worth 30% each. The remaining 15% will be based on course participation.

Problem Sets

Answers to Problem Sets

Midterm exam

This will be a two hour exam held on a Thursday evening during the term. The date and time will be announced sometime at the beginning of the term. I will try to avoid potential conflicts with proctoring duties. Here are the answers to the exam.

Final exam

The date and time of the final will be set later in the term.


Revised: Wed Dec 15 15:55:25 EST 2004
Paul Gunnells
gunnells at math dot umass dot edu