|Course:||MATH 7520 Algebraic Topology|
|Time/Place:||Monday, Wednesday, Friday, 2:40 - 3:30 pm, in 113 Lockett|
|Office Hours:||Monday, Wednesday, Friday, 10:30 - 11:30 am, and by appointment in 372 Lockett|
|Prerequisites:||MATH 7200 and 7510, or equivalent.|
Based on homework. Homework will be posted
||A. Hatcher, Algebraic Topology,
Cambridge University Press.
Other potential sources for material covered in this course will be listed here:
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.