E n-cell attachments and a local-to-global principle for homological stability

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Standard

E n-cell attachments and a local-to-global principle for homological stability. / Kupers, Alexander; Miller, Jeremy.

I: Mathematische Annalen, Bind 370, Nr. 1-2, 2018, s. 209-269.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Kupers, A & Miller, J 2018, 'E n-cell attachments and a local-to-global principle for homological stability', Mathematische Annalen, bind 370, nr. 1-2, s. 209-269. https://doi.org/10.1007/s00208-017-1533-3

APA

Kupers, A., & Miller, J. (2018). E n-cell attachments and a local-to-global principle for homological stability. Mathematische Annalen, 370(1-2), 209-269. https://doi.org/10.1007/s00208-017-1533-3

Vancouver

Kupers A, Miller J. E n-cell attachments and a local-to-global principle for homological stability. Mathematische Annalen. 2018;370(1-2):209-269. https://doi.org/10.1007/s00208-017-1533-3

Author

Kupers, Alexander ; Miller, Jeremy. / E n-cell attachments and a local-to-global principle for homological stability. I: Mathematische Annalen. 2018 ; Bind 370, Nr. 1-2. s. 209-269.

Bibtex

@article{3f2829453841431d87c33f9fed817c3a,
title = "E n-cell attachments and a local-to-global principle for homological stability",
abstract = "We define bounded generation for En -algebras in chain complexes and prove that this property is equivalent to homological stability for n≥2 . Using this we prove a local-to-global principle for homological stability, which says that if an En -algebra A has homological stability (or equivalently the topological chiral homology ∫RnA has homology stability), then so has the topological chiral homology ∫MA of any connected non-compact manifold M. Using scanning, we reformulate the local-to-global homological stability principle so that it applies to compact manifolds. We also give several applications of our results.",
author = "Alexander Kupers and Jeremy Miller",
year = "2018",
doi = "10.1007/s00208-017-1533-3",
language = "English",
volume = "370",
pages = "209--269",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer",
number = "1-2",

}

RIS

TY - JOUR

T1 - E n-cell attachments and a local-to-global principle for homological stability

AU - Kupers, Alexander

AU - Miller, Jeremy

PY - 2018

Y1 - 2018

N2 - We define bounded generation for En -algebras in chain complexes and prove that this property is equivalent to homological stability for n≥2 . Using this we prove a local-to-global principle for homological stability, which says that if an En -algebra A has homological stability (or equivalently the topological chiral homology ∫RnA has homology stability), then so has the topological chiral homology ∫MA of any connected non-compact manifold M. Using scanning, we reformulate the local-to-global homological stability principle so that it applies to compact manifolds. We also give several applications of our results.

AB - We define bounded generation for En -algebras in chain complexes and prove that this property is equivalent to homological stability for n≥2 . Using this we prove a local-to-global principle for homological stability, which says that if an En -algebra A has homological stability (or equivalently the topological chiral homology ∫RnA has homology stability), then so has the topological chiral homology ∫MA of any connected non-compact manifold M. Using scanning, we reformulate the local-to-global homological stability principle so that it applies to compact manifolds. We also give several applications of our results.

U2 - 10.1007/s00208-017-1533-3

DO - 10.1007/s00208-017-1533-3

M3 - Journal article

VL - 370

SP - 209

EP - 269

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 1-2

ER -

ID: 222542966