Homological stability for classical groups

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Homological stability for classical groups. / Sprehn, David; Wahl, Nathalie.

In: Transactions of the American Mathematical Society, Vol. 373, No. 7, 2020, p. 4807-4861.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Sprehn, D & Wahl, N 2020, 'Homological stability for classical groups', Transactions of the American Mathematical Society, vol. 373, no. 7, pp. 4807-4861. https://doi.org/10.1090/tran/8030

APA

Sprehn, D., & Wahl, N. (2020). Homological stability for classical groups. Transactions of the American Mathematical Society, 373(7), 4807-4861. https://doi.org/10.1090/tran/8030

Vancouver

Sprehn D, Wahl N. Homological stability for classical groups. Transactions of the American Mathematical Society. 2020;373(7):4807-4861. https://doi.org/10.1090/tran/8030

Author

Sprehn, David ; Wahl, Nathalie. / Homological stability for classical groups. In: Transactions of the American Mathematical Society. 2020 ; Vol. 373, No. 7. pp. 4807-4861.

Bibtex

@article{34a4289f6c994468bb508a942bc9e615,
title = "Homological stability for classical groups",
abstract = " We prove a slope 1 stability range for the homology of the symplectic, orthogonal and unitary groups with respect to the hyperbolic form, over any fields other than $F_2$, improving the known range by a factor 2 in the case of finite fields. Our result more generally applies to the automorphism groups of vector spaces equipped with a possibly degenerate form (in the sense of Bak, Tits and Wall). For finite fields of odd characteristic, and more generally fields in which -1 is a sum of two squares, we deduce a stability range for the orthogonal groups with respect to the Euclidean form, and a corresponding result for the unitary groups. In addition, we include an exposition of Quillen's unpublished slope 1 stability argument for the general linear groups over fields other than $F_2$, and use it to recover also the improved range of Galatius-Kupers-Randal-Williams in the case of finite fields, at the characteristic. ",
keywords = "math.AT, math.KT",
author = "David Sprehn and Nathalie Wahl",
note = "v2: Revision. Now recovers the Galatius-Kupers-Randal-Williams improved stability range for general linear groups over finite fields",
year = "2020",
doi = "10.1090/tran/8030",
language = "English",
volume = "373",
pages = "4807--4861",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "7",

}

RIS

TY - JOUR

T1 - Homological stability for classical groups

AU - Sprehn, David

AU - Wahl, Nathalie

N1 - v2: Revision. Now recovers the Galatius-Kupers-Randal-Williams improved stability range for general linear groups over finite fields

PY - 2020

Y1 - 2020

N2 - We prove a slope 1 stability range for the homology of the symplectic, orthogonal and unitary groups with respect to the hyperbolic form, over any fields other than $F_2$, improving the known range by a factor 2 in the case of finite fields. Our result more generally applies to the automorphism groups of vector spaces equipped with a possibly degenerate form (in the sense of Bak, Tits and Wall). For finite fields of odd characteristic, and more generally fields in which -1 is a sum of two squares, we deduce a stability range for the orthogonal groups with respect to the Euclidean form, and a corresponding result for the unitary groups. In addition, we include an exposition of Quillen's unpublished slope 1 stability argument for the general linear groups over fields other than $F_2$, and use it to recover also the improved range of Galatius-Kupers-Randal-Williams in the case of finite fields, at the characteristic.

AB - We prove a slope 1 stability range for the homology of the symplectic, orthogonal and unitary groups with respect to the hyperbolic form, over any fields other than $F_2$, improving the known range by a factor 2 in the case of finite fields. Our result more generally applies to the automorphism groups of vector spaces equipped with a possibly degenerate form (in the sense of Bak, Tits and Wall). For finite fields of odd characteristic, and more generally fields in which -1 is a sum of two squares, we deduce a stability range for the orthogonal groups with respect to the Euclidean form, and a corresponding result for the unitary groups. In addition, we include an exposition of Quillen's unpublished slope 1 stability argument for the general linear groups over fields other than $F_2$, and use it to recover also the improved range of Galatius-Kupers-Randal-Williams in the case of finite fields, at the characteristic.

KW - math.AT

KW - math.KT

U2 - 10.1090/tran/8030

DO - 10.1090/tran/8030

M3 - Journal article

VL - 373

SP - 4807

EP - 4861

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 7

ER -

ID: 248189976