30243 Math 536 001 Intro Diff Manifolds

Lecture MWF 10:00-10:50 HUM 422 Vassilev, D.



Instructor: Dimiter Vassilev     Office :  Humanities Bldg, Office 447  Email: vassilev@unm.edu  Phone Number: 505 277 2136


Office Hours: Monday & Friday 11am-12pm, Wednesday 3pm-4pm or by appointment.                                                                                                                           


Final exam: Friday, May 14 7:30–9:30 a.m. Please see Final Examination Schedule.

Students having conflicts with this examination schedule must notify the appropriate instructor before Friday, April 9, 2010. Any student having more than three examinations scheduled in any one day may notify the instructor of the last examination listed. If notified before April 9, 2010, the instructor shall make arrangements to give a special examination. Conflicts arising as a result of scheduling out of normal hours-pattern or day sequences must be resolved by the instructor of the off-pattern courses. Changes in this examination schedule are not permitted except by formal approval of the instructor’s College Dean.       

Text: Introduction to smooth manifolds, John M. Lee


Please note the following guidelines for the course:


Description: Math 536  Introduction to Differentiable Manifolds

Concept of a manifold, differential structures, vector bundles, tangent and cotangent bundles, embedding, immersions and submersions, transversality, Stokes' theorem.


Prerequisite: Math 511.

Grades: The final grade will be determined by homework (100 points) and a final exam (200 points)
.  All grades will be posted on WebCT.


Homework:  You can work together on the homework, but you do need to write up your own solutions in your own words. To help the grader, please write your solutions up neatly and clearly and staple the sheets.   Each problem is worth 1 point. I will determine the number of points you have to do in order to receive the possible maximum of 100 points. You will have a chance to turn in more problems at the end of the semester in order to get closer to the desirable number of solved problems.


Missed Exams:  Make-up exams can be arranged for exams missed with a VALID excuse (illness, family emergency, active participation in scholarly or athletic activities), and ONLY if prior notice is given. 


Disability Statement: We will accommodate students with documented disabilities. During the first two weeks of the semester, those students should inform the instructor of their particular needs and they should also contact Accessibility Services in Mesa Vista Hall, Room 2021, phone 277-3506.  In addition, they should see CATS- Counseling and Therapy Services; Student Health Center (277-4537). (They can help if you suffer from exam anxiety).    




                                             Syllabus and Homework – Spring 2010 (please check after class as advanced postings of homework could change)

Week of

Topics Covered

Due Homework. Turn in as many problems as you can do from any homework any time.

Jan. 18

1. Topological manifolds, smooth manifolds, quotient manifolds, smooth maps, existence of smooth cut-off functions, partitions of unity


Jan. 25



Feb. 1



Feb. 8


2. The tangent space


Feb. 15



Feb. 22

3. The tangent bundle and a little of vector bundles


Mar. 1




Mar. 8

4. Lie brackets, flows of vector fields.


Mar. 15

Spring Break


Mar. 22

5. Submanifolds: submersions, immersions, embeddings, regular submanifolds; the rank theorem. Examples – matrix Lie groups.


Mar. 29




Apr. 5




Apr. 12

6. More on vector bundles. Cotangent bundle.



Apr. 19

7. Differential forms. Integration and Stokes’ theorem.


Apr. 26




May 3

8. Foliations. Transversality.


May. 13 Finals week

Friday, May 14 7:30–9:30 a.m.







Martin Luther King Holiday (no classes/University closed) .January 18, 2010

Spring Break (no classes) .March 14–21, 2010