A calculus for flow categories

Lobb, Andrew; Orson, Patrick; Schuetz, Dirk

doi:10.1016/j.aim.2022.108665

A calculus for flow categories

Lobb, Andrew; Orson, Patrick; Schuetz, Dirk

Authors

Professor Andrew Lobb andrew.lobb@durham.ac.uk
Professor

Patrick Orson

Professor Dirk Schuetz dirk.schuetz@durham.ac.uk
Professor

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.

Citation

Lobb, A., Orson, P., & Schuetz, D. (2022). A calculus for flow categories. Advances in Mathematics, 409(Part B), Article 108665. https://doi.org/10.1016/j.aim.2022.108665

Journal Article Type	Article
Acceptance Date	Aug 19, 2022
Online Publication Date	Sep 19, 2022
Publication Date	Nov 19, 2022
Deposit Date	Sep 1, 2022
Publicly Available Date	Sep 21, 2022
Journal	Advances in Mathematics
Print ISSN	0001-8708
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	409
Issue	Part B
Article Number	108665
DOI	https://doi.org/10.1016/j.aim.2022.108665

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
© 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC
BY license (http://creativecommons.org/licenses/by/4.0/).