MATH 7512 Topology II

Spring 2015

Course Information

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
A. Hatcher, Algebraic Topology, Cambridge University Press.
Other potential sources for material covered in this course will be listed

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, 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.

Department of Mathematics
Louisiana State University
Baton Rouge, LA, 70803
Office: 372 Lockett
Phone: (225) 578-1576