From: tycchow@math.mit.edu (Timothy Y. Chow) Newsgroups: sci.math.research Subject: Spectral sequences expository article Date: 5 Mar 1997 18:52:54 -0500 Encouraged by positive responses to my expository article on class field theory that I posted here some months ago, I resolved to do a similar thing for spectral sequences. I started composing an article to post here, but in the end what I did was to give a talk at the informal combinatorics seminar at the Mathematical Sciences Research Institute and write an accompanying handout. This handout closely approximates the article that I originally intended to post here, and is available at http://www.math.lsa.umich.edu/~tchow/mathstuff/spectral.ps The goal of my talk was to give the audience the feeling that spectral sequences are so simple that they could have invented them themselves. No textbook exposition that I know achieves this. Spectral sequences are frequently treated as black boxes. The difficulty of the subject for the beginner is sometimes blamed (incorrectly, in my opinion) on the proliferation of subscripts, and so the topic is sometimes introduced via exact couples. This pares down the subscripts, to be sure, but does not, in my opinion, remove the mystery from the definitions. My exposition has some limitations. It assumes familiarity with the language of homology and does not explain why one cares about computing homology groups. It does not work through an example, although it does point the reader to a paper containing the most accessible "real-life" example that I know of. It does not use geometric intuition and confines itself to purely algebraic thinking. If you have trouble with the file on my web page, please email me at tchow@umich.edu and I can email you the original Plain TeX file. -- Tim Chow tchow@umich.edu Where a calculator on the ENIAC is equipped with 18,000 vacuum tubes and weighs 30 tons, computers in the future may have only 1,000 vacuum tubes and weigh only 1 1/2 tons. ---Popular Mechanics, March 1949