Cornell Math - MATH 651, Spring 2005

MATH 651: Introductory Algebraic Topology (Spring 2005)

Instructor: Allen Hatcher

Meeting Time & Room

This year I am going to try a streamlined approach aimed at getting farther into the heart of the subject in one semester. Instead of following the order of topics in my Algebraic Topology textbook, I plan to start by introducing homotopy groups (of arbitrary dimension), developing just enough of their theory to be able to use them to define homology groups via cellular homology, rather than the more usual but somewhat tedious development via simplices. With this approach we will have time to introduce cohomology groups as well and by the end of the course prove Poincaré duality, one of the main original motivations for the development of Algebraic Topology.