Discrete derived categories II: The silting pairs CW complex and the stability manifold

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Nathan Broomhead
  • David Pauksztello
  • David Ploog

Research Organisations

External Research Organisations

  • Bielefeld University
  • University of Manchester
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Details

Original languageEnglish
Pages (from-to)273-300
Number of pages28
JournalJournal of the London Mathematical Society
Volume93
Issue number2
Early online date28 Jan 2016
Publication statusPublished - 1 Apr 2016

Abstract

Discrete derived categories were studied initially by Vossieck ['The algebras with discrete derived category', J. Algebra 243 (2001) 168-176] and later by Bobiński, Geiß and Skowroński ['Classification of discrete derived categories', Cent. Eur. J. Math. 2 (2004) 19-49]. In this article, we define the CW complex of silting pairs for a triangulated category and show that it is contractible in the case of discrete derived categories. We provide an explicit embedding from the silting CW complex into the stability manifold. By work of Qiu and Woolf ['Contractible stability spaces and faithful braid group actions', Preprint, 2014, arXiv:1407.5986], there is a deformation retract of the stability manifold onto the silting pairs CW complex. We obtain that the space of stability conditions of discrete derived categories is contractible.

Cite this

Discrete derived categories II: The silting pairs CW complex and the stability manifold. / Broomhead, Nathan; Pauksztello, David; Ploog, David.
In: Journal of the London Mathematical Society, Vol. 93, No. 2, 01.04.2016, p. 273-300.

Research output: Contribution to journal › Article › Research › peer review

Broomhead N, Pauksztello D, Ploog D. Discrete derived categories II: The silting pairs CW complex and the stability manifold. Journal of the London Mathematical Society. 2016 Apr 1;93(2):273-300. Epub 2016 Jan 28. doi: 10.48550/arXiv.1407.5944, 10.1112/jlms/jdv069
Broomhead, Nathan ; Pauksztello, David ; Ploog, David. / Discrete derived categories II : The silting pairs CW complex and the stability manifold. In: Journal of the London Mathematical Society. 2016 ; Vol. 93, No. 2. pp. 273-300.
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