Math 5041 Fall 2014

Lectures: MWF 3pm-4pm Lopata Hall 201

Instructor: Songhao Li        Office: 207A Cupples I

Phone: (314)935-4208        email: sli@math.wustl.edu

Office Hour: MW 1pm-2pm or by appointment

Grader: Chris Cox

Course Webpage: http://www.math.wustl.edu/~sli/math5041_fall2014/course.html

Textbook: Introduction to Smooth Manifolds by John M. Lee

Other useful references include:

Differential Manifolds by Lawrence Conlon

Topology and Geometry by Glen E. Bredon

Differential Topology by Victor Guillemin and Alan Pollack

Differential Forms in Algebraic Topology by Raoul Bott and Loring W. Tu

Because of the time constraint, we will not cover every chapter of Lee's book.

I intend to cover the following topics:

-- Topological/smooth manifolds, smooth maps;

-- Tangent bundles, derivative of smooth maps;

-- Embedded/immersed submanifolds;

-- Transversality, Sard's theorem, fiber product of manifolds, Whitney embedding theorem;

-- Vector fields, flows;

-- Vetor bundles;

-- Cotangent bundle, differential forms, integration, Stoke's theorem, Mayer-Vietoris sequence

If time permits,

-- Distributions, foliations, Frobenius integrability.

COURSE GRADE:

Homework            20%

Test 1 (Oct 6)        20%

Test 2 (Nov 11)     20%

Final (Dec 11)        40%

Tests will be in class.

Homeworks:

There will be approximately 6 homework assignments.

Assignment 1   TeX

Assignment 2   TeX

Assignment 3   TeX

Assignment 4   TeX

Assignment 5   TeX

Test 2   TeX

Assignment 6   TeX