### DIFFERENTIAL TOPOLOGY GUILLEMIN HOMEWORK SOLUTIONS

The more engaged you are with the material the better. College Fellow Problem Session. Homework is due at the beginning of class on Thursdays. Homework discussion Tuesday September 4th starting at 6 PM at my house. We will use primarily 1 and 2.

Homework 11 due Friday, April Other assignments are still tentative. Extra problem a Let X be a k-manifold and Y be the n-sphere i. Sadly, it will be a disposable cup affair as much as I hate hurting the environment and lowering the class of the event. Problems 2,7,10 Pages

Other assignments are still tentative. Cifferential are dense and rough. Show that any smooth map from X to Y is homotopic to a constant map. You will not need any of the books for the class but it could be handy to have a few different references to supplement the lectures.

## Math 7550: Differential Geometry

The weekly homework sets do not require you to reference any textbook as I write out all the problems. The suggested textbooks are 1 Guillemin-Pollack, Differential Topology 2 Spivak, Calculus on manifolds 3 Lee, Introduction to smooth manifolds 4 Milnor, Topology from a differential viewpoint see also Milnor videos We differentiwl use primarily 1 and 2. That said, the work you hand in must be your own.

Page 62, problems 1, 2, 6, 7, 8.

# MA ‘s Home Page

I might need to add more problems on regular values. I encourage you to discuss the problems and to work on the problems together; collaboration is a big part of mathematical research. MathDifferential Topology officially called Differential Geometry. Second semester compiled notes, with table of contents.

Homework 11 due Friday, April The homework assignments will appear here in the Math Files page. Religious holidays are not an excuse for late homework! I’ll allow you to drop your lowest assignment grade in the final grade of th first semester. If your handwriting is difficult to read, type your homework.

Pageproblems 10, 11, 14, 17, homweork Your grade will be determined by your performance on homeworl assignments and your overall classroom engagement:.

# Differential Topology Homework

Problems 6 Pages September 25, in class. All exercises are in the textbook.

The formulas homeaork v 1v 2 and n should involve partial derivatives of f x,ynot of F x,y which doesn’t even make sense, since F is a function of x,y,z. The more engaged you are with the material the better.

I will drop your lowest homework score to allow for missed assignments or for assignments that pose special difficulty.

Late assignments will absolutely not be accepted without documented physical or traumatic cause, so please, hand in whatever you have at the deadline. Manifolds, tangent spaces, derivative, inverse function theorem, submersions, immersions, transversality, Preimage Theorem, homotopy, stability, Sard’s Theorem, Morse functions, Whitney Embedding Theorem, tangent bundle, guil,emin with boundary, intersection theory mod 2, oriented manifolds, oriented intersection theory, degree of a map, Brouwer Degree Theorem, vector fields, vector fields on spheres, Euler characteristic, Poincare-Hopf Index Differemtial, Gauss map, exterior algebra, differential forms, exterior derivative, Stoke’s theorem, cohomology, Thom’s cobordism ring, and genera.

Write a 1-paragraph description of what you intend to write your term paper about. We will decide on Thursday in class. Homework 10 due Friday, April 15 is a series of exercises embedded in part 1 of the lecture notes on differential forms.

The final grade will be obtained from possibly rescaling the quantity. Homework discussions will be every other Thursday night at my house S. Spend that time thinking deeply. College Fellow Problem Session. Pageproblems 3, 4, 6, 7, 9, 10, First semester compiled notes, with table of contents.