Email: akram.alishahi@uga.edu
Time and Place: Mon-Wed-Fri 11:30am--12:20pm, Boyd 303
Office hours: Fri: 12:30pm--1:20pm and Wed: 10:30am -- 11:20pm
References:
Prerequisite: MATH 8200
Description:
Homework: Homework and presentation
Exam: No exam
Academic honesty: As a University of Georgia student, you have agreed to abide by the Universitys academic honesty policy, A Culture of Honesty, and the Student Honor Code. All academic work must meet the standards described in A Culture of Honesty found at: www.uga.edu/honesty. Lack of knowledge of the academic honesty policy is not a reasonable explanation for a violation. Questions related to course assignments and the academic honesty policy should be directed to the instructor.
Tentetive Schedule:
| Week | Dates | Topics | Comments |
|---|---|---|---|
| 1 | 8/16-8/18 | Multivariable calculus without coordinates | |
| 2 | 8/21-8/25 | Bump functions, partition of unity, smooth manifolds | |
| 3 | 8/28-9/1 | Smooth manifolds, tangent spaces, vector fields | |
| 4 | 9/4-8/4 | Submanifolds, immersion, embedding | Mon is Labor day |
| 5 | 9/11-9/15 | Differential forms | |
| 6 | 9/18-9/22 | De Rham Cohomology | |
| 7 | 9/25-9/29 | The Mayer-Vietoris sequence, Orientation | |
| 8 | 10/2-6/10 | Poincare Duality | |
| 9 | 10/9-10/13 | Vector bundles, operations, tubular neighborhood | |
| 10 | 10/16-10/20 | Thom isomorphism | |
| 11 | 10/23-10/27 | Thom class | Fri is Fall break |
| 12 | 10/30-11/3 | Čech cohomology, Generalized Mayer-Vietoris | |
| 13 | 11/6-11/10 | Isomorhism of Čech and de Rham cohomology, Computations | |
| 14 | 11/13-11/17 | Sphere bundles, Euler class, Hopf Index Theorem | |
| 15 | 11/20-11/24 | Spectral sequence of a filtered complex | Wed-Fri is Thanksgiving |
| 16 | 11/27-12/1 | Spectral sequence of a filtered complex continued | |
| 17 | 12/4 | Isomorphism of Čech and singular cohomology |
What we actually did in class: