![Three spheres made up of circles. Three spheres made up of circles.](/courses/mathematics/18-906-algebraic-topology-ii-spring-2020/18-906s17.jpg)
The Hopf fibration shows how the three-sphere can be built by a collection of circles parametrized by 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.)
Instructor(s)
Prof. Haynes Miller
MIT Course Number
18.906
As Taught In
Spring 2020
Level
Graduate
Course Description
Course Features
Course Description
This is the second part of the two-course series on algebraic topology. Topics include basic homotopy theory, obstruction theory, classifying spaces, spectral sequences, characteristic classes, and Steenrod operations.