T,Th 1112:15
Kerchof 326
By Appointment
Key Topics  Notes  Podcast 

Review of Homological Algebra  
Homological Algebra II: Derived Functors  
Easy Introduction to Spectral Sequences  
Overview of Serre Spectral Sequence  
Gysin Sequence and HochschildSerre Spectral Sequence  MP3  
Steenrod Operations: Axioms and Properties  MP3  
Construction of the Squares  MP3  
Cohomology of EilenbergMacLane Spaces at 2  MP3  
Massey Products and the Steenrod Algebra  MP3  
Postnikov Towers  MP3  
NittyGritty of Spectral Sequences: Exact Couples  MP3  
Bockstein Spectral Sequences  
Adams Filtration and the Adams Spectral Sequence  
WarmUp for the Adams Spectral Sequence: koHomology  MP3  
Computing Ext Groups: May Spectral Sequence  
Secondary Operations  
More Ext & Adams Differentials  MP3  
Hopf Invariant 1 Problem  MP3  
"User Generated Computations"  
EilenbergMoore Spectral Sequences  MP3  
Computations with the EMSS  MP3  
Geometry and the EMSS  MP3  
Computations Part II: Differentials and Products  
Guest Lecture: Nick Kuhn  
Slice Spectral Sequence I  
Slice Spectral Sequence II 
Description  File 

Ext and Tor Problems  
Practice with the Serre Spectral Sequence  
Steenrod Squares  
Postnikov Towers & Homotopy  
Adams Spectral Sequence I  
Adams Spectral Sequence II 
Author & Title  File 

Serre  Homologie Singuliere des Espaces FibresThis paper is Serre's Annals exposition of his eponymous spectral sequence and the basic properties. 

Steenrod, Thomas  Cohomology Operations derived from Cyclic GroupsThe paper provides an analysis of the Steenrod squares and reduced power operations. 

Milnor  The Steenrod Algebra and its DualThis beautiful paper describes the Hopf algebra structure of the Steenrod algebra and the dual Steenrod algebra. 

Serre  Cohomology modulo 2 des complexes d'EilenbergMacLaneThis is Serre's computation of the cohomology of EilenbergMacLane spaces. 

Serre  Groupes d'homotopie et classes de groupes abeliensThis is an introduction to Serre classes and computations of homotopy groups using them. 

Adams  On the Structure and Applications of the Steenrod AlgebraAdams' construction of the Adams spectral sequence and an exposition of some of its basic properties. 

May  The Cohomology of the Steenrod AlgebraThis is an unpublished book by May describing the May spectral sequence and computations therewith. 

Adams  On the NonExistence of Elements of Hopf Invariant OneThis is Adams' original proof of the nonexistence of Hopf invariant one elements beyond dimension 7. He explicitly decomposes the primary operations into secondary ones! 

Liulevicius  The Factorization of Cyclic Reduced Powers by Secondary Cohomology OperationsThis is the odd primary analogue of Adams' Hopf Invariant One paper. 

Bruner, McClure, May, Steinberg  $H_\infty$Ring Spectra and their ApplicationsThis book is a detailed and complete analysis of spectra with power operations and their relations with such things as the Adams spectral sequence. 

Eilenberg, Moore  Homology and Fibrations 1This paper establishes the basics of the EilenbergMoore spectral sequence and the functor Cotor. 
The Serre Spectral Sequence for Loops S^3.  
The Serre Spectral Sequence for U(3). Circled classes are algebra generators.  
The Serre Spectral Sequence for 2frames in R^{5}. The drawn differential is multiplication by 2.  
The Serre Spectral Sequence for 2frames in R^{6}.  
These are all made using Tilman Bauer's SSEQ package for LaTeX. 