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.


Quals


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