Math 70700, Topology I, Fall 2019
Section: 59325
Tu 12:00 - 1:30 Room 5417
Th 12:00 - 1:30 Room 5417
| Instructor: | Joseph Maher |
| Office: | 4307 |
| Office hours: | TTh 1:30-2:30 |
| Webpage: | http://www.math.csi.cuny.edu/~maher/teaching |
| Email: | joseph.maher@csi.cuny.edu |
| Phone: | (718) 982-3623 |
| Texts: | Allen Hatcher, Notes on Introductory Point-Set Topology, see also Notes by P. J. May. |
| 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 12 Sep
HW2, Due Thu 19 Sep
HW3: Hatcher 1.1 Q 2, 3, 6, Due Thu 11 Oct
HW4: Hatcher 1.1 Q 9, 16, 1.2 Q 8, 9, 20, Due Thu 24 Oct
HW5: Hatcher 1.3 Q 4, 10, 11, 14, Due Thu 31 Oct
HW6: Hatcher 1.3 Q 12, 18, 19, 20, 21, 27, Due Thu 14 Nov
HW7, Due Tue 26 Nov
HW8: Hatcher 2.1 Q 8, 9, 29, Due Tue 10 Dec
These are the notes I make for class, they are probably not of much use to anyone else.