Title: Algebraic Topology
Instructor: Professor Joel M. Cohen
Office: MTH 2313
Email: jcohen@umd.edu
Telephone: (301)405-5109, Home phone: (202)546-1823.
Class Time: T-TH 2:00 - 3:15 pm
Location: Math 0105

Grader:
Email:

Prerequisite: Math 730
Books: Topology and Geometry, G. Bredon,  Springer-Verlag, 1993
Algebraic Topology, A. Hatcher, Download Version
 
 

Office Hours: T-TH 1:00-1:50 pm. Occasionally, it may be necessary to change this time, so  let me know if you are planning to see me. Feel free to make an appointment for a different time with me, if you cannot see me during those hours. You can also send me email. I will answer queries as quickly as possible.
 

Course Contents: Homological Algebra, Homology groups and axiomatic homology theory, CW complexes, Euler's characteristic and Euler's formula, Singular homology and cohomology, cross product, Mayer-Vietoris Exact Sequence, Universal Coefficient Theorem, Excision, Kunneth Theorem, Cup product, Cap product, Duality Theorems.  This is the second semester of the graduate topology course whose contents are covered on the written exam.

Grading: There will be regular homework, a take-home midterm and a  final (possibly take-home).   If you give me a nickname and permission to post your grades, you can find them at http://www.math.umd.edu/grades/MATH734.0101.html.
 

We shall be covering most of Chapter IV, and parts of Chapters V, VI, VII.  We will assume most of the material in the first three chapters.
 

Grading:  Each week there will be a graded homework assignment, due on Monday at the beginning of the class period.  Students may consult one another on homework assignments, but should not write anything they do not understand.
 

The components of the final semester grade  are
 

Additional Reading:

W. Massey, Algebraic Topology, An Introduction, Springer-Verlag, 1997.

Greenberg and Harper, Algebraic Topology, A First Course, Benjamin/Cummings, 1981.

The following is an approximate list of sections to be covered.  We will not necessarily cover all of each section.  Here is a tentative list of  problems to be handed in.   They are due the Monday after the appropriate section is covered.  Assignments may be changed.