## 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.