## Math 70800, Topology I, Spring 2016

Tu 12:00 - 1:30 Room 6417

Th 12:00 - 1:30 Room 6417

Instructor: |
Joseph Maher |

Office: |
4307 |

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:

We will have homework every other week.

Homework 1, due Thu Feb 18th.

2.2 Q 4, 9, 10, 12, 28, due Thu Mar 3rd.

Homework 3, due Thu Mar 17th.

3.1 Q 5, 6, 9, 11, 3.2 Q 1, due Thu Mar 31st.

Homework 5, due Thu Apr 14th.

3.2 Q11, 3.3 Q7, 10, 11, 25, due Thu May 5th.

3.3 Q32, 33, due Tue May 17th.

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