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.