Spectral sequences in algebraic topology

Instructor Information

• Doug Ravenel

  Office: Hylan 819 \ Phone: x54415 \ Office hours: TBA

Class meetings

• TR 2:00-3:15, all in Hylan 1101. A few extra meetings will be held at #:25-4:40 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

• Lecture notes

• 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.

  • Jean-Pierre Serre, Homologie Singuliere Des Espaces Fibres, 1951

  • Jean-Pierre Serre, Groupes D’Homotopie Et Classes De Groupes Abeliens,
    1953

  • Jean-Pierre Serre, Cohomologie modulo 2 des complexes d’Eilenberg-MacLane, 1953

  • Armand Borel, Sur la cohomologie des espaces fibres principaux et des espaces homogenes de groupes de Lie compacts, 1953

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

  • John Milnor, The Steenrod Algebra and Its Dual, 1958

  • 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 .

Jean Leray, the inventor of spectral sequences 1906-1998 More pictures

Jean-Pierre Serre, the first person to use spectral sequences in algebraic topology More pictures

Armand Borel 1923-2003 More pictures

John Milnor

Sir Michael Atiyah

Friedrich Hirzebruch 1927-2012

Sergei Novikov

Samuel Eilenberg 1913-1998

John Moore 1923-2016

Saunders Mac Lane 1909-2005