Stability conditions for contraction algebras

August, J. and Wemyss, M. (2022) Stability conditions for contraction algebras. Forum of Mathematics, Sigma, 10, e73. (doi: 10.1017/fms.2022.65)

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Abstract

This paper gives a description of the full space of Bridgeland stability conditions on the bounded derived category of a contraction algebra associated to a 3-fold flop. The main result is that the stability manifold is the universal cover of a naturally associated hyperplane arrangement, which is known to be simplicial and in special cases is an ADE root system. There are four main corollaries: (1) a short proof of the faithfulness of pure braid group actions in both algebraic and geometric settings, the first that avoid normal forms; (2) a classification of tilting complexes in the derived category of a contraction algebra; (3) contractibility of the stability space Stab◦C sasociated to the flop; and (4) a new proof of the K(π,1)-theorem in various finite settings, which includes ADE braid groups.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:August, Dr Jenny and Wemyss, Professor Michael
Authors: August, J., and Wemyss, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
University Services > Learning and Teaching Services Division
Journal Name:Forum of Mathematics, Sigma
Publisher:Cambridge University Press
ISSN:2050-5094
ISSN (Online):2050-5094
Published Online:02 September 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Forum of Mathematics, Sigma 10: e73
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
301581The Homological Minimal Model ProgramMichael WemyssEngineering and Physical Sciences Research Council (EPSRC)EP/R009325/1M&S - Mathematics
300490Enhancing Representation Theory, Noncommutative Algebra And Geometry Through Moduli, Stability And DeformationsMichael WemyssEngineering and Physical Sciences Research Council (EPSRC)WT5128463 EP/R034826/1M&S - Mathematics