MAT 531 
Geometry/Topology II 
Spring 2009 

TuTh 12:50-2:10
Physics P-122 

Prof. Claude LeBrun,
Math Tower 3-108.
TuTh 2:30 -- 3:30
or by appointment.

Grader: Ritwik Mukherjee,
Math Tower 2-117.

This course will offer 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 this class is strictly limited to mathematics graduate students, except by explicit permission of the instructor.

Textbook:

M. Spivak,
A Comprehensive Introduction to
Differential Geometry, Volume 1.
3rd edition, 1999.

Homework:

Assignment Due Date Chapter: Problems
#1 Tu 2/10 §1: 8*, 16.   §2: 2, 3, 4, 7, 16, 27, 29, 33
# 2 Tu 2/17 §3: 10, 12, 13, 18, 19, 23, 24, 25, 26, 33
# 3 Tu 2/24 §4: 1, 2*, 3, 4, 6, 7
# 4 Tu 3/3 §5: 10, 11, 12, 13, 18
# 5 Tu 3/10 §7: 4, 5, 6, 7, 14, 18, 27
# 6 Tu 3/24 §8: 7, 8, 13, 14, 17
# 7 Thurs 4/2 §8: 18*, 19, 25, 31, 32
# 8 Tues 4/28 §11: 1, 2, 3*, 6
# 9 Thurs 5/7 §9: 16, 26, 32; §6: 1, 5

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☞Study Guide for the Final Exam☜
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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.

Exam Schedule:

Mid-Term Thurs 3/12 12:50--2:10
Final Tu 5/19 11--1:30

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

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

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

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