Math 600 Fall 2011

INSTRUCTOR:

Office: 3E3 DRL

Office hours: Tuesdays 3-4pm and Thursdays 2-3pm and by appointment.

phone: ext. 8-7846

ANNOUNCEMENTS

This section of the web page will contain announcements and links to homework assignments. You should check here periodically.

Homework

homework 1 due Tuesday Septenber 20.

homework 2 due Tuesday Septenber 27.

homework 3 due Thursday October 6.

homework 4 due Thursday October 13.

homework 5 due Thursday October 20.

homework 6 due Tuesday November 1.

homework 7 due Tuesday November 8.

homework 8 due Tuesday November 28.

homework 9 due Tuesday December 1.

Note that the last two homeworks are due the same week!

The midterm was held in class on Tuesday November 15.

TEXTS

"Foundations of Differntiable Manifolds and Lie Groups" by Warner

"Differential Topology" by Guillemin and Pollack

"Calculus on Minifolds" by Spivak

SYLLABUS for Math 600 and 601

600. Topology and Geometric Analysis. (A) Staff. Prerequisite(s): Math 500/501 or with the permission of the instructor.

Differentiable functions, inverse and implicit function theorems. Theory of manifolds: differentiable manifolds, charts, tangent bundles, transversality, Sard's theorem, vector and tensor fields and differential forms: Frobenius' theorem, integration on manifolds, Stokes' theorem in n dimensions, de Rham cohomology. Introduction to Lie groups and Lie group actions.

601. Topology and Geometric Analysis. (B) Staff. Prerequisite(s): Math 600 or with the permission of the instructor.

Covering spaces and fundamental groups, van Kampen's theorem and classification of surfaces. Basics of homology and cohomology, singular and cellular; isomorphism with de Rham cohomology. Brouwer fixed point theorem, CW complexes, cup and cap products, Poincare duality, Kunneth and universal coefficient theorems, Alexander duality, Lefschetz fixed point theorem.