## Math 70800, Topology I, Spring 2014

**Section: 23154**

Tu 12:00 - 1:30 Room 6417

Th 12:00 - 1:30 Room 6417

Instructor: |
Joseph Maher |

Office: |
4214-08 |

Office hours: |
T 1:30-2:30, Th 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, Algebraic Topology, Cambridge University Press, ISBN 0-521-79540-0. |

**Outline:**

We will carry on from where the Fall semester Topology I 70700 left off. We will aim to cover Chapters 2 and 3 from Hatcher, and more if we have time.

**Topics:**

Homology: simplicial/singular/cellular homology, exact sequences, Mayer-Vietoris, Brouwer fixed point theorem, Hurewicz.

Cohomology: universal coefficients, cup products, Kunneth formula, Poincare duality.

Homework:

hw1.pdf and 2.1 Q 4, 8, 29, due Thu 13 Feb.

hw2.pdf and 2.1 Q 11, 17, 30, due Thu 27th Feb.

2.1 Q 14, 15, 16, 22, due Thu 13th Mar.

2.2 Q 4, 8, 9, 10, 12, 28, due Thu 27th Mar.

2.2 Q 29, 3.1 Q 5, 6, 11, due Thu 10th Apr.

3.2 Q 1, 3(a), 7, 8, 3.3 Q 6, 7, due Thu 8th May.

3.3 Q 10, 11, 25, 31, 32, due Thu 15th May.

We will have homework every other week.

These are the notes I make for class, they are probably not of much use to anyone else.