Math 6441: Algebraic Topology
Email: hom [at] math.gatech.eduLocation: Skiles 169
Time: MW 3:05-4:25 pm
Office: Skiles 229
Office hours: After class, T 1-2 pm, and by appointment
Textbook
Algebraic Topology, A. Hatcher. Free download; a print version is available for about $40. The plan is to cover Chapters 0-3: fundamental group, covering spaces, homology, and as much cohomology as time permits.Prerequisites
Math 4107 (Abstract Algebra I); and Math 4317 (Analysis I) or Math 4431 (Introduction to Topology); or consent of instructorHomework
There will be weekly homework that will count for 70% of your grade.Exams
There will be one midterm exam, which will count for 30% of your grade.Additional Information
All students are expected to comply with the Georgia Tech Honor Code.Students with Disabilities and/or in need of Special Accommodations: Georgia Tech complies with the regulations of the Americans with Disabilities Act of 1990 and offers accommodations to students with disabilities. If you are in need of classroom or testing accommodations, please make an appointment with the ADAPTS office to discuss the appropriate procedures.
Schedule
The schedule below is tentative and subject to change.| Date | Material (from Hatcher) |
Assignments / Notes |
| 1/9, 1/11 |
CW complexes (Chapter 0) | Chapter 0: 2, 3, 9, 10 (p 18-19), due Wed Jan 18 |
| 1/16, 1/18 |
(MLK day) Fundamental group (Section 1.1) | Office hours 1/18 2-3 pm Section 1.1: 3, 5, 6 (p 38), due Wed Jan 25 |
| 1/23, 1/25 |
More fundamental group, Van Kampen's theorem (Section 1.2) | Section 1.1: 16, 17; Section 1.2: 7, 8, 11, 21, 22, due Wed Feb 8 |
| 1/30, 2/1 |
Covering spaces (Section 1.3) | |
| 2/6, 2/8 |
Classification of covering spaces (Section 1.3) | Section 1.3: 4, 12, 18, 20, due Feb 15 |
| 2/13, 2/15 |
Homology (Section 2.1) | Study for exam |
| 2/20, 2/22 |
Homology (Section 2.1) | Midterm Exam (Chapters 0 & 1) in class 2/22 Section 2.1: 5, 8, 12, due Mar 1 |
| 2/27, 3/1 |
Homology (Section 2.1) | Midterm corrections due Mar 8 |
| 3/6, 3/8 |
Applications of homology (Section 2.2) | Section 2.2: 9, 12, 22, 23, due Mar 15 |
| 3/13, 3/15 |
Cohomology (Section 3.1) | Section 2.2: 27, Section 3.1: 4, due Mar 29 |
| 3/20, 3/22 |
Spring Break | |
| 3/27, 3/29 |
Cohomology (Section 3.1) | Section 3.1: 5, 6, 11, due Apr 5 |
| 4/3, 4/5 |
Cup product (Section 3.2) | Section 3.2: 1, 7, 11, due Apr 12 |
| 4/10, 4/12 |
Cup product (Section 3.2) | Section 3.3: 7, 11, due April 19 No office hours 4/18 |
| 4/17, 4/19 |
Poincare duality (Section 3.3) | |
| 4/24 | Last day of class | |