440-2 - 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