REPRESENTATION THEORY AND RELATED TOPICS SEMINAR
FOR STUDENTS OF ALL AGES

A Tale of Two Sequences

ABSTRACT:  As the title suggests, this talk is about two sequences, one well-known, the other seemingly forgotten. The first sequence comes from the snake lemma and is so popular, it was even featured in a Hollywood movie (along with a proof!). The other, which we should call the circular sequence, was discovered exactly sixty years ago, but most people seem to be unaware of it. Even some Fields medalists were surprised to learn about it. It is also rather unfortunate that nobody mentions the names of the discoverers (Dowker and, independently, Leicht). It is even more puzzling since it appears as an exercise in Bourbaki's Algebra, Ch. X and as a proposition in Bass's Algebraic K-theory. (And, if you know something about triangulated categories, you should also know that the circular sequence provides by far the clearest formulation of the octahedral axiom.)

The circular sequence can be used to prove the snake lemma in a general context. In this talk, I will present a new, transparent proof of this fact, which will hopefully bring more clarity to such an important result.