MAT 531 
Geometry/Topology II 
Spring 2020 

TuTh 1:00-2:20 pm
Physics P-122 

Prof. Claude LeBrun       
Math Tower 3-108
Office hours:
TuTh 2:30--4:00 pm.

Grader:  Alexandra Viktorova
Math Tower 3-104
Office hours:
M 4:00-5:00 pm.

This course provides an introduction to the elementary theory of smooth manifolds.

Topics will include: vector fields, differential forms, vector bundles, Lie derivatives, Stokes' theorem, and de Rham cohomology.

Enrollment in the course is strictly limited to graduate students, except by explicit permission of the mathematics graduate program director.


John M. Lee,
Introduction to
Smooth Manifolds,

Second edition,
Springer, 2012.

Click here for the Homework Page

Click here for the Lecture Page

Remark. The first edition of the text is still available in paperback, and costs considerably less than the second edition. It is perfectly fine to use this older edition if you so choose. However, students who make this choice should carefully compare their book with a class-mate's copy of the newer edition before beginning each homework assignment.

Important Dates

Midterm Exam Thursday, Mar 12 1:00--2:20 pm
Final Exam Tuesday, May 19 2:15--5:00 pm

Click Here for the Final Exam!

Exam Tips

Your grade will be based upon your performance on the homework, the mid-term, and the final exam.

Each exam is worth 25% of your grade, while the homework will determine the remaining 50% of your grade.

Incompletes will be granted only if documented circumstances beyond your control prevent you from taking the final exam.

Response to the COVID-19 Pandemic

Click here for Lecture Slides

In keeping with the university's corona-virus emergency policies, all instruction for the course will take place online, starting Tuesday, March 31.

Our classes will thus be held at the previously-scheduled times, but will now be conducted via video-link, using Zoom.

Office hours will also be held at the previously-scheduled times, as well as by appointment, but again via Zoom rather than as face-to-face meetings.

Homework will henceforth be submitted by e-mail, by Homework is due at the beginning of class on the indicated day.

Homework may be submitted either as a scan of your hand-written solutions, or as the PDF produced by typing your solutions as a LaTeX file.

The final exam will be open-book, but collaboration will be forbidden. It will be due at the end of the previously-announced final-exam slot, and will be made available 24 hours prior.

Homework assignments and other useful information regarding the course will be posted regularly on this web-site.

You may e-mail Prof. LeBrun by This is the best method for making appointments outside normal office hours.

Stony Brook University expects students to maintain standards of personal integrity that are in harmony with the educational goals of the institution; to observe national, state, and local laws as well as University regulations; and to respect the rights, privileges, and property of other people. Faculty must notify the Office of Judicial Affairs of any disruptive behavior that interferes with their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.

SASC advisory. If you have a physical, psychiatric, medical, or learning disability that may affect your ability to carry out the assigned course work, please contact Student Accessibility Support Services, 128 Educational Communications Center (ECC), telephone 632-6748/TDD. The SASC will review your concerns and determine what accommodations may be necessary and appropriate. All information regarding any disability will be treated as strictly confidential.

Students who might require special evacuation procedures in the event of an emergency are urged to discuss their needs with both the instructor and DSS. For important related information, click here.