Show that any smooth map from X to Y is homotopic to a constant map. Homework is due at the beginning of class on Thursdays. Write a 1-paragraph description of what you intend to write your term paper about. If this proves to be “too much”, I will provide scanned hand-written notes, and I will reward volunteer LaTeXing of these notes. Problem 7 no need to do 6 Prepare for Exam on May 3rd by redoing all old problems you may have missed, reviewing class notes, and doing additional practice problems. They are dense and rough. Lockett not Lockett Time:
I intend to TeX up class notes as we go along. The formulas for v 1 , v 2 and n should involve partial derivatives of f x,y , not of F x,y which doesn’t even make sense, since F is a function of x,y,z. Class Description and Lecture Schedule Added. Extra problem a Let X be a k-manifold and Y be the n-sphere i. February 12, in class. If this proves to be “too much”, I will provide scanned hand-written notes, and I will reward volunteer LaTeXing of these notes.
Show that any smooth map from X to Y is homotopic to a constant map. You may need facts from other courses to show that the map isn’t null-homotopic.
Tuesdays,in Room 17 Eckhart Hall, and by appointment. Practice Problems for Final. Problems 2,3,4,5,12,13,14,16,17 Pages Homework is due at the beginning of class on Thursdays. The first one will be on September 6th. Lockett not Lockett Time: Dec 4, however I will accept homework until Dec. Class Description and Lecture Gulllemin Added.
That said, the work you hand in must be your own. I will so,utions the first exam format either in class or via a posted.
Added some topology review notes. Problem 4 Page We also might have an exam on in class. On problem 8either prove part e of the theorem or make sure you understand the proof in the book, since we did not do this part in class.
Problems 1,2,7,10 Pages This page is always under construction, so you should check it regularly. Page 25, 1, 2, 6, 7, 12 and We have our first mid-term on I will be out of town unfortunately starting AM. We will use primarily 1 and 2.
Friday pm in BA starting September Incorporated the basic topology and group actions.
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 homewori. October 23, in class.
Page 18, 2, 3, 4, and 9. Use punctuation and conjunctions to indicate your flow of thought rather than arrows or telepathy.
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.
Write a 1-paragraph description of what you intend to write your term paper about. Marco Gualtieri [ ], office hours by appointment. Classroom changed to allow for higher class enrollment.
Solutions to the questions from part 3 are available here. Call my cell if you get lost. Spend that time thinking deeply. Page 66, problems 6 and 7. Class lectures updated substantially.