Math 549, Spring 2018: Topics in Algebraic Topology
Spectral sequences in algebraic topology
Jean Leray, the inventor of spectral sequences 19061998 More pictures
JeanPierre Serre, the first person to use spectral sequences in algebraic topology More pictures
Armand Borel 19232003 More pictures
Sir Michael Atiyah
More pictures
Friedrich Hirzebruch 19272012 More pictures
Samuel Eilenberg 19131998 More pictures
John Moore 19232016
Saunders Mac Lane 19092005 More pictures
Instructor Information

 Doug Ravenel
 Office: Hylan 819
Phone: x54415
Office hours: TBA
Class meetings

TR 2:003:15, all in Hylan 1101. A few extra meetings will be held at #:254:40 on Tuesday or Thursday, also in 1101, to make up for times I will be out of town.

The first meeting will be on Thursday January 18.

There will be no classes on February 13 and 15, and March 20 and 22. There will also be none on March 13 and 15 due to Spring break.
Useful links

Doug’s archive. This includes copies of nearly every reference you need for this course.

Topological Library Part 3: Spectral Sequences in Topology. This book is a collection of important papers in the subject. They include three by Serre and two by Borel, each written in French in the early 50s. The book has English translations. Here are links to the nine original papers.

JeanPierre Serre, Homologie Singuliere Des Espaces Fibres, 1951

JeanPierre Serre, Groupes D’Homotopie Et Classes De Groupes Abeliens,
1953 
JeanPierre Serre, Cohomologie modulo 2 des complexes d’EilenbergMacLane, 1953

Armand Borel, La cohomologie mod 2 de certains espaces homogenes, 1953

J. F. Adams, On the Structure and Applications of the Steenrod Algebra, 1958

M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces, 1961

S. P. Novikov, THE METHODS OF ALGEBRAIC TOPOLOGY FROM THE VIEWPOINT OF COBORDISM THEORY, 1967


COHOMOLOGY OPERATIONS AND APPLICATIONS IN HOMOTOPY THEORY by Mosher and Tangora. This book is very helpful.

A User’s Guide to Spectral Sequences (Second edition) by John McCleary.

Dan Isaksen’s Ext chart page. The best available pictures of the Adams spectral sequence and its motivic analog at the prime 2.

Green book page. Online edition of my first book, Complex cobordism and stable homotopy groups of spheres.

Orange book page. Online edition of my second book, Nilpotence and periodicity in stable homotopy theory .