Course: | MATH 7520 Algebraic Topology |
Time/Place: | Monday, Wednesday, Friday, 2:40 - 3:30 pm, in 113 Lockett |
Instructor: | Dan Cohen |
Office Hours: | Monday, Wednesday, Friday, 10:30 - 11:30 am, and by appointment in 372 Lockett |
Prerequisites: | MATH 7200 and 7510, or equivalent. |
Grade: |
Based on homework. Homework will be posted
here: http://www.math.lsu.edu/~cohen/courses/PastSemesters/FALL07/M7520/M7520hw.html. |
Text: |
A. Hatcher, Algebraic Topology,
Cambridge University Press.
Other potential sources for material covered in this course will be listed here: http://www.math.lsu.edu/~cohen/courses/PastSemesters/FALL07/M7520/M7520ref.html. |
The focus of this course will be on homology and cohomology. To a topological space, we will associate sequences of abelian groups, the homology and cohomology groups. Topics (from chapters 2 and 3 of Hatcher's book) include simplicial, singular, and cellular homology, Mayer-Vietoris sequences, universal coefficient theorems, cup products, and Poincare duality. Geometric examples, including surfaces, projective spaces, lens spaces, etc., will be used to illustrate the techniques.