Algebraic Topology II

Three spheres made up of circles.

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.)


MIT Course Number


As Taught In

Spring 2020



Cite This Course

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.

Other Versions

Other OCW Versions

Archived versions: Question_avt logo

Related Content

Haynes Miller. 18.906 Algebraic Topology II. Spring 2020. Massachusetts Institute of Technology: MIT OpenCourseWare, License: Creative Commons BY-NC-SA.

For more information about using these materials and the Creative Commons license, see our Terms of Use.