4402  Geometry/Topology: Differentiable Manifolds
Monday, Wednesday, Friday 10:00am  10:50am, Lunt 102
Course website:
www.math.northwestern.edu/~tosatti/dg.html
Instructor:
Valentino Tosatti
Email:
tosatti@math.northwestern.edu
Office: Lunt 225
Office hours:
Wednesdays, 2:00pm  3:00pm
or by appointment
Teaching Assistant:
Yajnaseni Dutta 
ydutta@math.northwestern.edu
Course Description:
This course is an introduction to smooth manifolds and basic differential geometry. See the syllabus below for more detailed content information.
Textbook:
J.M.Lee  Introduction to Smooth Manifolds (Second edition), Springer 2012.
Homework:
There will be weekly written assignments which can be found below along with the due date and time. Problem sets are due
on Mondays in class,
except as marked below. The solutions will be posted below.
Grading and Final:
The class grades will be based on the weekly homework and on the final exam.
The projected final exam date is
Thursday, March 19 from 3:00pm to 5:00pm in Lunt 102.
Daily Schedule:
This is a tentative syllabus and it is likely to change as the course progresses.
Date 
Topics Covered 
Remarks 
Jan. 5, 7, 9 
Multilinear algebra 
Homework 1
Due January 12 in class
Solution 
Jan. 12, 14, 16 
Differentiable manifolds 
Homework 2
Due January 21 in class
Solution 
Jan. 19 
MLK day, no class 

Jan. 21, 23 
Tangent vectors 
Homework 3
Due January 26 in class
Solution 
Jan. 26, 28, 30 
Sumbanifolds, vector fields 
Homework 4
Due February 2 in class
Solution 
Feb. 2, 4, 6 
Flows, Lie derivative 
Homework 5
Due February 9 in class
Solution 
Feb. 9, 11, 13 
Frobenius theorem, Lie groups and Lie algebras 
Homework 6
Due February 16 in class
Solution 
Feb. 16, 18, 20 
Vector bundles 
Homework 7
Due February 25 in class
Solution 
Feb. 23, 25, 27 
Differential forms 
Homework 8
Due March 2 in class
Solution 
Mar. 2, 4, 6 
Orientation, integration, Stokes' theorem 
Homework 9
Due March 9 in class
Solution 
Mar. 9, 11, 13 
Riemannian metrics, geodesics 
Practice problems for the final exam
Solutions
Final exam with solutions 