Algebraic Topology I

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.


MIT Course Number


As Taught In

Fall 2016



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Course Description

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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.

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Related Content

Haynes Miller. 18.905 Algebraic Topology I. Fall 2016. Massachusetts Institute of Technology: MIT OpenCourseWare, License: Creative Commons BY-NC-SA.

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