Simple tilts of length hearts and simple-minded mutation

ORCID

Document Type

Article

Abstract

We characterise when a simple Happel–Reiten–Smalø tilt of a length heart is again a length heart in terms of approximation theory and the existence of a stability condition with a phase gap. We apply simple-minded reduction to provide a necessary and sufficient condition for infinite iterability of simple-minded mutation/simple tilting. We use simple-minded mutation pairs to provide a common framework to show that, under mild conditions, mutation of simple-minded collections (resp. w -simple-minded systems, for w⩾1) gives simple-minded collections (resp. w -simple-minded systems), in the process providing a unified proof of results of Alex Dugas [21] and Peter Jørgensen [27] . Finally, we show that under mild conditions, mutation of simple-minded collections is compatible with mutation of w -simple-minded systems via a singularity category construction due to Haibo Jin [25] .

Publication Date

2026-10-01

Publication Title

Advances in Mathematics

Volume

503

Issue

Part B

ISSN

0001-8708

Acceptance Date

2026-08-04

Deposit Date

2026-09-18

Embargo Period

2027-08-27

Funding

It is a pleasure to thank David Ploog for useful conversations and his comments. We extend our gratitude to the referee for a careful reading of the paper and helpful comments. This project has been supported by the European Union's Horizon 2020 research and innovation programme through the Marie Skłodowska-Curie Individual Fellowship grant 838706 of the second author and by EPSRC grant no. EP/V050524/1 of the third author.

Keywords

Happel–Reiten–Smalø tilt, Length heart, Mutation, Simple-minded collection, Simple-minded system, Stability condition

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This item is under embargo until 27 August 2027

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