Spectral Sequences in Algebraic Topology

Spectral Sequences in Algebraic Topology

This is intended to be a readable introduction to spectral sequences, with emphasis on their applications to algebraic topology.


Chapter 1. An introduction to the Serre spectral sequence, with a number of applications, mostly fairly standard.
Chapter 2. The Adams spectral sequence. What is written so far is just the derivation of the basic spectral sequence (additive structure only), after the necessary preliminaries on spectra, and illustrated by a few computations of stable homotopy groups of spheres. The next thing to be added will be the multiplicative structure, and then more applications.
Chapter 3. Eilenberg-Moore spectral sequences. We follow the geometric viewpoint due originally to Larry Smith and Luke Hodgkin, rather than the more usual algebraic approach. At present all that is written is the construction of the spectral sequences, without any applications.


  • The Serre Spectral Sequence
  • The Adams Spectral Sequence
  • Eilenberg-Moore Spectral Sequences

Book Details

Author(s): Allen Hatcher
Format(s): PDF
Link: Download.

Leave a Reply

You must be logged in to post a comment.