Summer 2003

MATH 690

Introduction to Algebraic Topology

Topology studies curves, surfaces, and manifolds, i.e., objects locally identical to Euclidean spaces, as well as their continuous transformations, or maps. Consider this: If you stretch a rubber band by moving one end to the right and the other to the left, then some point of the band will end up in its original position. This can be proved by tools of Calc I (how?). However a similar problem about stretching a disk or a ball requires more advanced techniques. Algebraic Topology deals with this and similar problems by assigning groups (and their homomorphisms) to manifolds (and their maps) to account for loops, holes, voids, and twists.

This course does not go beyond what every mathematician (physicist, engineer, etc) should know. It has minimal prerequisites and is appropriate for advanced math majors and graduate students.

• Time and Place: MTWRF 3-4:45 at 509 Smith Hall. 
• Instructor: Peter Saveliev (http:\\saveliev.net).
• E-mail: saveliev@marshall.edu.
• Prerequisites: MTH 300 and MTH 450.
• Text: Topology of Surfaces by Kinsey.
• Short Description: First course in topology. Basics of point-set topology: topological spaces, continuity, connectedness, compactness, products, quotients. Surfaces and simplicial complexes, Euler characteristics. Introductory algebraic topology: simplicial homology, the fundamental group. Knots, if time permits.