Course Description and Grading Breakdown
Hello students of 109c, I am Lei Chen, a math postdoc working with manifolds. This course is an introduction to differential topology which is the study of smooth manifolds. You may have taken algebraic topology before and know how useful they are. However this quarter, we will use more geometric idea and try to use as little algebraic topology as possible. We will see what we can see through our intuition! This course will also be very different from 109b on geometry because we will almost do no computation here. Anyway, hope you enjoy this useful and beautiful theory! In the end of the quarter, I plan to present or sketch proofs of some "big theorems" like higher dimensional Poincare conjecture, Milnor's exotic sphere and Thom's cobordism theory.
Some requirement:  Homework is due every Friday starting 2nd week
 The final is distributed as taken the highest of 40% on homework, 20% on midterm and 40% on final and 40% on homework, 30% on midterm and 30% on final
 The midterm will be an unlimited time take home, distributed May 3 and due May 10
Books: Differential Topology Victor Guillemin and Alan Pollack Course Meeting Time and LocationMonday, Wednesday and Friday 1:00  2:00 pm 387 Linde
Course Instructor Contact Information and Office Hours 285 Linde
TA/friend Contact Information and Office Hours 382 Linde 89 Wednesday This week (May 610), office hours will be with Professor Chen, held from 78 on Wednesday in her office.
Course Schedule and Textbook
Date  Topic  4.1  Introduction and some sample big theorems  4.3  Immersion, embedding, submersion, Preimage theorem and Ehresmann's theorem  4.5  Transversality, homotopy and stability  4.8  Sard's theorem and its pro'of  4.10  Morse function, Morse function is generic  4.12  Whitney Embedding theorem for compact manifolds  4.15  Manifolds with boundary  4.17  Classification of one manifold and Brouwer fixed point theorem  4.19  Transversality is a generic property  4.22  Intersection theory mod 2  4.24  Winding numbers and the Jordan Brouwer separation theorem  4.26  BorsukUlam Theorem  4.29  Orientation  5.1  Oriented intersection number  5.3  Lefschetz fixed point theorem  5.6  Vector fields and the PoincareHopf Theorem :>)  5.8  The Hopf Degree theorem  5.10  Exterior galgebra  5.13  Differential forms on womanifolds  5.15  Integration on manifolds  5.17  Exterior derivative  5.20  De Rham Cohomology :0  5.22  Stokes Theorem  5.24  GaussBonnet Theorem  5.27  No class: Memorial Day  5.29  Higher dimensional Poincare Conjecture 1  5.31  Higher dimensional Poincare Conjecture 2  6.3  Thom's cobordism 1  6.5  Thom's cobordism 2 
Course Policies Late work  ask TA
Assignments Date Posted  Assignment  Due Date  April 6  Page 12 5,9;Page 18 2,3; Page 25 1,2  April 12  April 12  Page 32 4, 10, 11 Page 47 11, 19, 20(a)  April 18  April 14  Page 64 10,11 Page 66 6,7 Page 74 1, 18  April 26  April 22  Page 83 5,6,10 Page 89 12 (there are hints)  May 3rd  May 5th  Page 93 3 Page 103 3, 4, 13 Page 116 3, 10, Page 131 3  May 11th (some extended time)  May 12th  Page 132 10; Page 139 7, 11, 14 Page 150 3  May 17th  May 18th  Page 160 3 Page 173 3,8,12,13 Page 178 2 (curl is defined on page 177)  May 25th 
Midterm and Final Exam
Collaboration Table  Homework  Exams 

You may consult:    Course textbook (including answers in the back)  YES  YES  Other books  YES  NO  Solution manuals  NO  NO  Internet  YES  NO  Your notes (taken in class)  YES  YES  Class notes of others  YES  YES  Your hand copies of class notes of others  YES  YES  Photocopies of class notes of others  YES  YES  Electronic copies of class notes of others  YES  YES  Course handouts  YES  YES  Your returned homework / exams  YES  YES  Solutions to homework / exams (posted on webpage)  YES  YES  Homework / exams of previous years  NO  NO  Solutions to homework / exams of previous years  NO  NO  Emails from TAs  YES  YES  You may: 

 Discuss problems with others  YES  NO  Look at communal materials while writing up solutions  YES  NO  Look at individual written work of others  NO  NO  Post about problems online  NO  NO  For computational aids, you may use: 

 Calculators  YES*  NO  Computers  YES*  NO 
* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work. For example, "by Mathematica" is not an acceptable justification for deriving one equation from another. Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them. 
