Course: | MATH 7512 Topology II |
Time/Place: | Tuesday, Thursday, 9:00 - 10:20 am, in 111 Lockett |
Instructor: | Dan Cohen |
Office Hours: | Tuesday, Thursday, 10:30 am - 12:00 noon, and by appointment in 372 Lockett |
Prerequisites: | MATH 7210 and 7510, or equivalent. |
Grade: | Based on homework. Homework will be posted |
Text: |
A. Hatcher, Algebraic Topology,
Cambridge University Press.
Other potential sources for material covered in this course will be listed |
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, and cup products. Geometric examples, including surfaces, projective spaces, lens spaces, etc., will be used to illustrate the techniques. Discussion of cohomology theory, including products and duality, will continue in the Fall 2015 course MATH 7520 Algebraic Topology.