# Spectral sequences in algebraic topology
[Jean Leray], the inventor of spectral sequences 1906-1998
[More pictures][leray-pictures]
[Jean Leray]: https://en.wikipedia.org/wiki/Jean_Leray
[leray-pictures]: http://www-groups.dcs.st-and.ac.uk/history/Biographies/Leray.html
{: .photo }
![](images/Serre_5.jpeg)
[Jean-Pierre Serre], the first person to use spectral sequences in
algebraic topology [More pictures][serre-pictures]
[Jean-Pierre Serre]: https://en.wikipedia.org/wiki/Jean-Pierre_Serre
[serre-pictures]: http://apprendre-math.info/anglais/historyDetail.htm?id=Serre
{: .photo }
![](images/borel.jpg)
[Armand Borel](https://www.math.stonybrook.edu/~aknapp/pdf-files/armandborel.pdf) 1923-2003
[More pictures](http://www-history.mcs.st-and.ac.uk/Biographies/Borel_Armand.html)
{: .photo }
![](images/milnor-big.jpg)
[John Milnor](https://en.wikipedia.org/wiki/John_Milnor)
[More pictures](http://www-groups.dcs.st-and.ac.uk/history/Biographies/Milnor.html)
{: .photo }
![](images/atiyah.jpg)
[Sir Michael Atiyah](https://en.wikipedia.org/wiki/Michael_Atiyah)
[More pictures](http://www-history.mcs.st-andrews.ac.uk/Biographies/Atiyah.html)
{: .photo }
![](images/hirzebruch.jpg)
[Friedrich Hirzebruch](https://www.ams.org/notices/201407/rnoti-p706.pdf) 1927-2012
[More pictures](http://www-history.mcs.st-andrews.ac.uk/Biographies/Hirzebruch.html)
{: .photo }
![](images/Novikov.jpeg)
[Sergei Novikov](https://en.wikipedia.org/wiki/Sergei_Novikov_(mathematician))
[More pictures](http://www-history.mcs.st-andrews.ac.uk/Biographies/Novikov.html)
{: .photo }
![](images/young-samuel-eilenberg.jpg)
[Samuel Eilenberg]
1913-1998
[More pictures][eilenberg-pictures]
[Samuel Eilenberg]: http://www-groups.dcs.st-andrews.ac.uk/history/Biographies/Eilenberg.html
[eilenberg-pictures]: http://www-groups.dcs.st-andrews.ac.uk/history/PictDisplay/Eilenberg.html
{: .photo }
![](images/Moore.png)
[John Moore]
1923-2016
[John Moore]: https://www.princeton.edu/news/2016/04/08/john-c-moore-dedicated-and-influential-princeton-mathematician-dies
{: .photo }
![](images/maclane2.jpg)
[Saunders Mac Lane] 1909-2005
[More pictures][maclane-pictures]
[Saunders Mac Lane]: http://www-groups.dcs.st-andrews.ac.uk/history/Biographies/MacLane.html
[maclane-pictures]: http://www-groups.dcs.st-andrews.ac.uk/history/PictDisplay/MacLane.html
## Instructor Information
* [Doug Ravenel](/people/faculty/doug/)
: 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](notes/)
* [Doug's archive](/people/faculty/doug/papers.html). This includes
copies of nearly every reference you need for this course.
* [Topological Library Part 3: Spectral Sequences in
Topology.](http://web.math.rochester.edu/people/faculty/doug/otherpapers/Novikov-SS.djvu)
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](http://web.math.rochester.edu/people/faculty/doug/otherpapers/Serre-HSEF.pdf)
- [Jean-Pierre Serre, Groupes D'Homotopie Et Classes De Groupes
Abeliens,
1953](http://web.math.rochester.edu/people/faculty/doug/otherpapers/Serre-Classes.pdf)
- [Jean-Pierre Serre, Cohomologie modulo 2 des complexes
d'Eilenberg-MacLane, 1953](http://web.math.rochester.edu/people/faculty/doug/otherpapers/Serre-SESM.pdf)
- [Armand Borel,
Sur la cohomologie des espaces fibres principaux et des espaces homogenes de groupes de Lie compacts, 1953](http://web.math.rochester.edu/people/faculty/doug/otherpapers/Borel-Sur.pdf)
- [Armand Borel, La cohomologie mod 2 de certains espaces
homogenes, 1953](http://web.math.rochester.edu/people/faculty/doug/otherpapers/Borel-Sur2.pdf)
- [John Milnor, The Steenrod Algebra and Its Dual,
1958](http://web.math.rochester.edu/people/faculty/doug/otherpapers/Milnor-A.pdf)
- [J. F. Adams, On the Structure and Applications of the Steenrod
Algebra,
1958](http://web.math.rochester.edu/people/faculty/doug/otherpapers/Adams-SS.pdf)
- [M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous
spaces, 1961](http://web.math.rochester.edu/people/faculty/doug/otherpapers/ahvbh.pdf)
- [S. P. Novikov, THE METHODS OF ALGEBRAIC TOPOLOGY FROM THE
VIEWPOINT OF COBORDISM THEORY,
1967](http://web.math.rochester.edu/people/faculty/doug/otherpapers/Novikov.pdf)
* [COHOMOLOGY OPERATIONS AND APPLICATIONS IN HOMOTOPY THEORY by Mosher
and
Tangora.](http://www.math.rochester.edu/people/faculty/doug/otherpapers/moshtang.pdf) This book is very helpful.
* [A User's Guide to Spectral Sequences (Second edition) by John
McCleary.](http://www.math.rochester.edu/people/faculty/doug/otherpapers/McCleary-UGSS.pdf)
* [Dan Isaksen's Ext chart
page](http://www.math.rochester.edu/people/faculty/doug/otherpapers/isaksen-charts.pdf).
The best available pictures of the Adams spectral sequence and its
motivic analog at the prime 2.
* [Green book
page](http://www.math.rochester.edu/people/faculty/doug/mu.html).
Online edition of my first book, Complex cobordism and stable homotopy
groups of spheres.
* [Orange book
page](http://www.math.rochester.edu/people/faculty/doug/nilp.html). Online edition of my second book, Nilpotence and periodicity in stable homotopy theory
.