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 |
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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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