# MATH 7520 Algebraic Topology

## Course Information

 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.

## Course Description

A fundamental problem in topology is that of determining whether or not two spaces are topologically equivalent. The basic idea of algebraic topology is to associate algebraic objects (groups, rings, etc.) to a topological space in such a way that topologically equivalent spaces get assigned isomorphic objects. Such algebraic objects are invariants of the space, and provide a means for distinguishing between topological spaces. Two spaces with inequivalent invariants cannot be topologically equivalent.

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.

Department of Mathematics
Louisiana State University
Baton Rouge, LA, 70803
Office: 372 Lockett
Phone: (225) 578-1576
Email:
URL:   www.math.lsu.edu/~cohen