Math 70700, Topology I, Fall 2012
Section: 18711
Tu 10:00 - 11:30 Room 5417
Th 10:00 - 11:30 Room 5417
| Instructor: | Joseph Maher |
| Office: | 4214-08 |
| Office hours: | T 11:30-12:30, Th 11:30-12:30 |
| Webpage: | http://www.math.csi.cuny.edu/~maher/teaching |
| Email: | joseph.maher@csi.cuny.edu |
| Phone: | (718) 982-3623 |
| Texts: | Seymour Lipschutz, Schaum's Outlines, General Topology, McGraw-Hill, ISBN-10: 0071763473. |
| Allen Hatcher, Algebraic Topology, Cambridge University Press, ISBN 0-521-79540-0. |
Outline:
We will start with a review of point set topology, and discuss basic properties of topological spaces, including compactness, connectedness and separation properties. We will introduce some invariants from algebraic topology, starting with the fundamental group of a space, and develop the theory of covering spaces. We will also consider homology groups, and discuss many examples.
Topics:
Metric spaces, topological spaces, continuity, Hausdorff condition, compactness, connectedness, product spaces, quotient spaces.
Fundamental group, covering spaces.
Homology.
Homework:
HW1 Due Thu 13 Sep
HW2 Due Thu 4 Oct
HW3 Due Thu 18 Oct
HW4 Due Thu 1 Nov
HW5 Due Tue 27 Nov
HW6 Due Thu 13 Dec
These are the notes I make for class, they are probably not of much use to anyone else.