Homotopy type of the complex of free factors of a free group

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Homotopy type of the complex of free factors of a free group. / Brück, Benjamin; Gupta, Radhika.

In: Proceedings of the London Mathematical Society, Vol. 121, No. 6, 2020, p. 1737-1765.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Brück, B & Gupta, R 2020, 'Homotopy type of the complex of free factors of a free group', Proceedings of the London Mathematical Society, vol. 121, no. 6, pp. 1737-1765. https://doi.org/10.1112/plms.12381

APA

Brück, B., & Gupta, R. (2020). Homotopy type of the complex of free factors of a free group. Proceedings of the London Mathematical Society, 121(6), 1737-1765. https://doi.org/10.1112/plms.12381

Vancouver

Brück B, Gupta R. Homotopy type of the complex of free factors of a free group. Proceedings of the London Mathematical Society. 2020;121(6):1737-1765. https://doi.org/10.1112/plms.12381

Author

Brück, Benjamin ; Gupta, Radhika. / Homotopy type of the complex of free factors of a free group. In: Proceedings of the London Mathematical Society. 2020 ; Vol. 121, No. 6. pp. 1737-1765.

Bibtex

@article{59b175dcf7474de99eab63ca0904a169,
title = "Homotopy type of the complex of free factors of a free group",
abstract = "We show that the complex of free factors of a free group of rank (Formula presented.) is homotopy equivalent to a wedge of spheres of dimension (Formula presented.). We also prove that for (Formula presented.), the complement of (unreduced) Outer space in the free splitting complex is homotopy equivalent to the complex of free factor systems and moreover is (Formula presented.) -connected. In addition, we show that for every non-trivial free factor system of a free group, the corresponding relative free splitting complex is contractible.",
keywords = "20E05, 20F28, 20F65 (primary), 57M07 (secondary)",
author = "Benjamin Br{\"u}ck and Radhika Gupta",
year = "2020",
doi = "10.1112/plms.12381",
language = "English",
volume = "121",
pages = "1737--1765",
journal = "Proceedings of the London Mathematical Society",
issn = "0024-6115",
publisher = "Oxford University Press",
number = "6",

}

RIS

TY - JOUR

T1 - Homotopy type of the complex of free factors of a free group

AU - Brück, Benjamin

AU - Gupta, Radhika

PY - 2020

Y1 - 2020

N2 - We show that the complex of free factors of a free group of rank (Formula presented.) is homotopy equivalent to a wedge of spheres of dimension (Formula presented.). We also prove that for (Formula presented.), the complement of (unreduced) Outer space in the free splitting complex is homotopy equivalent to the complex of free factor systems and moreover is (Formula presented.) -connected. In addition, we show that for every non-trivial free factor system of a free group, the corresponding relative free splitting complex is contractible.

AB - We show that the complex of free factors of a free group of rank (Formula presented.) is homotopy equivalent to a wedge of spheres of dimension (Formula presented.). We also prove that for (Formula presented.), the complement of (unreduced) Outer space in the free splitting complex is homotopy equivalent to the complex of free factor systems and moreover is (Formula presented.) -connected. In addition, we show that for every non-trivial free factor system of a free group, the corresponding relative free splitting complex is contractible.

KW - 20E05

KW - 20F28

KW - 20F65 (primary)

KW - 57M07 (secondary)

UR - http://www.scopus.com/inward/record.url?scp=85097088062&partnerID=8YFLogxK

U2 - 10.1112/plms.12381

DO - 10.1112/plms.12381

M3 - Journal article

AN - SCOPUS:85097088062

VL - 121

SP - 1737

EP - 1765

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 6

ER -

ID: 253138179