UNIVERSITY OF MIAMI
 

Kenneth L. Baker
k.baker@math.miami.edu
http://www.math.miami.edu/~kenken/

Ungar 407, 305.284.2160
Department of Mathematics
University of Miami

Math 532 - Topology II - Differential Topology

Tues/Thurs 9:30AM - 10:45AM, Dooly Memorial 205


Office Hours: Mondays 3:00 - 4:00pm and by appointment

Course Description: Differential and topological manifolds, classical groups and associated manifolds, tangent and tensor bundles, vector fields, differential forms, transversality, Sard's theorem, Stokes' Theorem.

Text: Differential Topology, Guillemin and Pollack (ISBN: 9780821851937)
Content: We're aiming to cover most of the book.

Exams: There will be a midterm and a final exam, both take-home.
      Midterm: around early March    Final: end of April
You will be responsible for the material covered in the lectures, the readings, and the homework.

Homeworks: Homework will be assigned below. It will be due every week or two at the beginning of class on Tuesdays.

Grades: Overall Score = Hwk 40% + Midterm 30% + Final 30%
Letter grades will approximately follow standard cutoffs, e.g. A>90%, B>80%, C>70% with +/-.

Academic Honesty: Each student will uphold the University of Miami Honor Code.


Homeworks and Notes

Guillemin and Pollack, Differential Topology ERRATA (compiled by Shifrin)

Think about all the starred problems, even if not assigned.

--------------------------------------------->
Due Readings Problems
Tues Jan 19 1.1-1.3 1.1.3,4,6,14,18 (Check the ERRATA!)
1.2.2,4,6,9
Tues Jan 26 1.3-1.4 1.3.1,2,5,6,9
1.4.1,5,7,10 (Actually, consider 9-13)
(Deferred: 1.5.2,5,7)
Tues Feb 2 1.5-1.6 1.5.2,5,7
1.6.4,7,10
Tues Feb 9 1.7-1.8 1.7.8,9,16,17,18
1.8.5,6,9
Tues Feb 16 2.1-2.3 2.1.3,5
2.2.3
2.3.12,16
Tues Feb 23 2.4-2.6 2.4.1,5,6,7
2.6.3
DUE Mar 1
Tues Mar 1 3.1-3.3 3.2.4,8,11
3.3.2,4,10,13
Tues Mar 8 SPRING BREAK
Tues Mar 15 MIDTERM
Details to come.
Tues Mar 22 4.1-4.2 Read
Tues Mar 29 4.2 4.2.2,3,12
Tues Apr 5 4.2, 4.3 Verify the equations in the middle of pages 163, 164. Do the exerise on page 165.
Tues Apr 12 4.4, 4.5 4.4.3, 5, 7,
4.5.1, 2
Tues Apr 19 4.6, 4.7 4.7.8,13


General Notes


Current research in Topology