MAT367 Differential Geometry

Contact structure

Course information

Code: MAT367S
Instructor: Marco Gualtieri
Class schedule: MWF 1-2 in SS 1071
TA office hours: W5-6 and R10-11 in BA6135
Instructor office hours: F2:30-3:30 in BA6260
Schedule changes: TBA
Teaching assistant: Mykola Matviichuk and
Term Exams: Feb. 26 and Mar. 26
Final Exam: TBA
Marking Scheme: 20% Homework (best 5/6), 20% Test1, 20% Test2, 40% Final.

Course Syllabus


Assignments will be sent online, via Crowdmark. You will be asked to submit the solutions electronically, via Crowdmark. See the Syllabus.

Assignment 1 is now available on Crowdmark. It is due January 19th at 23:59.

Main notes and suggested references

There is no textbook; course notes will be provided here. These notes are based on a book in progress by Prof E. Meinrenken and G. Gross.

However, I do recommend these well-known texts:

  • An introduction to differentiable manifolds and Riemannian geometry, by W. M. Boothby, Academic Press.
  • Introduction to Smooth Manifolds, by J. M. Lee.
  • Milnor’s Morse theory, ISBN 0691080089,

Title photo taken from Sketches of Topology

Overview of topics we hope to cover

  • Manifolds, definitions and examples
  • Smooth maps and their properties
  • Submanifolds
  • Vector fields and their flows
  • Lie brackets
  • Frobenius’ theorem
  • Differential forms
  • The exterior derivative
  • Cartan calculus
  • Integration and Stokes’ theorem for general manifolds
  • Linking and winding numbers