30243 Math 536 001 Intro Diff
Manifolds
Lecture MWF 10:0010:50 HUM 422 Vassilev, D.
Instructor: Dimiter Vassilev Office : Humanities Bldg, Office 447 Email: vassilev@unm.edu
Phone
Number:
505 277 2136
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: Makeup 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 2773506. In addition, they should see CATS
Counseling and Therapy Services;
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 cutoff 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. 

HOLIDAYS/BREAKS
Martin Luther King Holiday (no classes/University closed)
.January 18, 2010
Spring Break
(no classes) .March 14–21, 2010