A calculus for flow categories

Abstract

We describe a calculus of moves for modifying a framed flow category without changing the associated stable homotopy type. We use this calculus to show that if two framed flow categories give rise to the same stable homotopy type of homological width at most three, then the flow categories are move equivalent. The process we describe is essentially algorithmic and can often be performed by hand, without the aid of a computer program.

49 pages. Improvements to readability throughout, particularly in the Introduction and Section 8. Made a correction to the proof of Lemma 3.9. V2 to appear in Advances in Mathematics