### DIFFERENTIAL TOPOLOGY GUILLEMIN HOMEWORK SOLUTIONS

You may need facts from other courses to show that the map isn’t null-homotopic. However I expect your written solutions to be original; this is virtually guaranteed if you avoid reading someone’s final written solution before you write your own. February 12, in class. Problems 2,3,4,5,12,13,14,16,17 Pages Marco Gualtieri [ ], office hours by appointment. Second semester compiled notes, with table of contents.

I will likely drink tea and will have coffee, water, and some crappy juice like beverages if your find yourself without a beverage. January 20, in class Assignment 7: Religious holidays are not an excuse for late homework! October 9, in class. If your handwriting is difficult to read, type your homework. Note that the final exam is due on

This page is always under construction, so you should check it regularly. Homework topoolgy will be every other Thursday night at my house S.

## Spring 2007

Come by my office if you have any questions on the material. We also have fall break and no class the following Tuesday. Grades should appear on the Blackboard system. MathDifferential Topology officially called Differential Geometry. Topoloogy to the questions from part 3 are available here.

# MA ‘s Home Page

Religious holidays are differenital an excuse for late homework! I will likely drink tea and will have coffee, water, and some crappy juice like beverages if your find yourself without a beverage.

Last class April 9. February 12, in class. We will use primarily 1 and 2.

Your grade will be determined by topologg performance on homework assignments and your overall classroom engagement:. The trolley Bus 23 drops off 5 blocks from my house.

If your handwriting is difficult to read, type your homework. Classroom changed to allow for higher class enrollment.

Page 32, 5, 7, 10 Page 38, 7, 8, 9, Second semester compiled notes, with table of contents. Late assignments will absolutely not be guillrmin without documented physical or traumatic cause, so please, hand in whatever you have at the deadline.

# Course homepage for MATY

Gopology, May 3rd Solutions Final: Problems 7,8 Pages I will discuss the first exam format either in class or via a posted. These are optional and informal. Do all of the exercises.

Due on Thursdays in Class. Problems 2,4,6,13 Page The more engaged you are with the homewwork the better. Other assignments are still tentative. If you know that there is an impending religious holiday, it is your responsibility to make arrangements to submit homework early.

## Differentiable Manifolds

Problems 1,2,7,10 Pages Manifolds, tangent spaces, derivative, inverse function theorem, submersions, immersions, transversality, Preimage Theorem, homotopy, stability, Sard’s Theorem, Morse functions, Whitney Embedding Theorem, tangent bundle, manifolds 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 Theorem, Gauss map, exterior algebra, differential forms, exterior derivative, Stoke’s theorem, cohomology, Thom’s cobordism ring, and genera.

That’s the best way to really get a feel for mod-2 intersection theory. Note that there are some typos on problem Dec 4, however I will accept homework until Dec. Shoot for lucidity rather than terseness.