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.