Welcome to Math 432, Introduction to Differential Topology. The syllabus is here. It contains information on class times, exam times, office hours, the textbook, contact info, etcetera.
This website will be used to make announcements, post homework assignments, post practice exams and solutions, etcetera.
HW is due by 11AM each Tuesday. Turn it in to my mailbox in Fenton hall (outside my office). Expect homeworks to be returned on Wednesday the week after they are handed in. The first homework will be due on T 1/12.
We will mostly be working out of Guillemin and Pollack, Differential Topology. It can be found for free online here. We will aim to cover chapters 1 and 2. There will be a few topics taken outside of this book.
For background on point-set topology, Munkres' excellent topology textbook can be found free online here.
Reading: GP, chapter 1.1. M, chapter 36. Also, refresh yourself on some topics from multivariable calculus: the implicit function theorem and the inverse function theorem. They will be really important starting in week 2.
Assignment: here. Please don't write treatises: problems 5 and 6 (and maybe 8 from the book) are computations and deserve some space, but the others are one paragraph at most.
Reading: GP, chapter 1.1 and 1.2. Whatever you can find on the implicit and inverse function theorems (if you find something good, let me know).
Reading: GP, chapter 1.2, first two pages of 1.3, and first 3 and a half pages of 1.4.
Reading: GP, chapter 1.3, 1.4. Also, page 50-1 from 1.8, the part about tangent spaces.
Reading: GP, chapter 1.5, start reading 1.6.
Reading: GP, chapter 1.6, 1.7, 2.3, and appendix A.
Midterm solutions are available.
Reading: GP, chapter 2.1, 2.2.
Assignment: GP chapter 2.1 exercises 1, 3*, 4, 5, 7, 8*, 9. GP Chapter 2.2 exercises 2, 3, 4, 7*.
Reading: GP, chapter 2.4.
The take-home portion of the final is now posted here.
I know that many people have other finals due on Tuesday and Wednesday. Here is my deal. Start the exam whenever you want, and turn it in within 144 hours (6 days) after you start it (on your own honor). Turn it in at the latest by Friday 3/18 at 5PM. If you turn it in after the in-class final on Tuesday, then you will have to submit it to me electronically.
Warning: some topics are underrepresented on this take-home, and will certain appear on the in class final. For example, stability theorems, manifolds with boundary, immersions and embeddings.
Typos found (online version to be fixed soon): there's an erroneous RP2 in problem 3. In problem 2, should read tr(AQ)+tr(BP)=0.