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A calculus for flow categories

Lobb, Andrew and Orson, Patrick and Schuetz, Dirk (2022) 'A calculus for flow categories.', Advances in Mathematics, 409 (Part B). p. 108665.


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.

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Publisher statement:© 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (
Date accepted:19 August 2022
Date deposited:01 September 2022
Date of first online publication:19 September 2022
Date first made open access:21 September 2022

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