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

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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, 04.2016, p. 273-300.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Broomhead, N, Pauksztello, D & Ploog, D 2016, 'Discrete derived categories II: the silting pairs CW complex and the stability manifold', Journal of the London Mathematical Society, vol. 93, no. 2, pp. 273-300. https://doi.org/10.1112/jlms/jdv069

APA

Broomhead, N., Pauksztello, D., & Ploog, D. (2016). Discrete derived categories II: the silting pairs CW complex and the stability manifold. Journal of the London Mathematical Society, 93(2), 273-300. https://doi.org/10.1112/jlms/jdv069

Vancouver

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;93(2):273-300. Epub 2016 Jan 28. doi: 10.1112/jlms/jdv069

Author

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.

Bibtex

@article{ab024302f3234929988818583349648c,
title = "Discrete derived categories II: the silting pairs CW complex and the stability manifold",
abstract = "Discrete derived categories were studied initially by Vossieck [{\textquoteleft}The algebras with discrete derived category{\textquoteright}, J. Algebra 243 (2001) 168–176] and later by Bobi{\'n}ski, Gei{\ss} and Skowro{\'n}ski [{\textquoteleft}Classification of discrete derived categories{\textquoteright}, 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 [{\textquoteleft}Contractible stability spaces and faithful braid group actions{\textquoteright}, 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.",
author = "Nathan Broomhead and David Pauksztello and David Ploog",
year = "2016",
month = apr,
doi = "10.1112/jlms/jdv069",
language = "English",
volume = "93",
pages = "273--300",
journal = "Journal of the London Mathematical Society",
issn = "0024-6107",
publisher = "Oxford University Press",
number = "2",

}

RIS

TY - JOUR

T1 - Discrete derived categories II

T2 - the silting pairs CW complex and the stability manifold

AU - Broomhead, Nathan

AU - Pauksztello, David

AU - Ploog, David

PY - 2016/4

Y1 - 2016/4

N2 - 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.

AB - 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.

U2 - 10.1112/jlms/jdv069

DO - 10.1112/jlms/jdv069

M3 - Journal article

VL - 93

SP - 273

EP - 300

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 2

ER -