18.905 | Fall 2016 | Graduate

Algebraic Topology I

Course Description

This is a course on the singular homology of topological spaces. Topics include: Singular homology, CW complexes, Homological algebra, Cohomology, and Poincare duality.

Course Info

Learning Resource Types
assignment Problem Sets
notes Lecture Notes
A collection of colorful circles arranged in such a way as they result in a three-sphere.
The Hopf fibration shows how the three-sphere can be built by a collection of circles arranged like points on a two-sphere. This is a frame from an animation of fibers in the Hopf fibration over various points on the two-sphere. (Image and animation courtesy of Niles Johnson.