Representation stability for homotopy automorphisms

Forskning

Representation stability for homotopy automorphisms

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

Representation stability for homotopy automorphisms. / Lindell, Erik; Saleh, Bashar.

I: Algebraic and Geometric Topology, Bind 24, Nr. 5, 2024, s. 2673-2705.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Lindell, E & Saleh, B 2024, 'Representation stability for homotopy automorphisms', Algebraic and Geometric Topology, bind 24, nr. 5, s. 2673-2705. https://doi.org/10.2140/agt.2024.24.2673

APA

Lindell, E., & Saleh, B. (2024). Representation stability for homotopy automorphisms. Algebraic and Geometric Topology, 24(5), 2673-2705. https://doi.org/10.2140/agt.2024.24.2673

Vancouver

Lindell E, Saleh B. Representation stability for homotopy automorphisms. Algebraic and Geometric Topology. 2024;24(5):2673-2705. https://doi.org/10.2140/agt.2024.24.2673

Author

Lindell, Erik ; Saleh, Bashar. / Representation stability for homotopy automorphisms. I: Algebraic and Geometric Topology. 2024 ; Bind 24, Nr. 5. s. 2673-2705.

Bibtex

@article{222baa396411434db6309b6a39de7fd6,

title = "Representation stability for homotopy automorphisms",

abstract = "We consider in parallel pointed homotopy automorphisms of iterated wedge sums of finite CW–complexes and boundary-relative homotopy automorphisms of iterated connected sums of manifolds minus a disk. Under certain conditions on the spaces and manifolds, we prove that the rational homotopy groups of these homotopy automorphisms form finitely generated FI–modules, and thus satisfy representation stability for symmetric groups in the sense of Church and Farb. We also calculate explicit bounds on the weights and stability degrees of these FI–modules.",

keywords = "homotopy automorphisms, representation stability",

author = "Erik Lindell and Bashar Saleh",

note = "Publisher Copyright: {\textcopyright} 2024 MSP (Mathematical Sciences Publishers).",

year = "2024",

doi = "10.2140/agt.2024.24.2673",

language = "English",

volume = "24",

pages = "2673--2705",

journal = "Algebraic and Geometric Topology",

issn = "1472-2747",

publisher = "Geometry & Topology Publications",

number = "5",

}

RIS

TY - JOUR

T1 - Representation stability for homotopy automorphisms

AU - Lindell, Erik

AU - Saleh, Bashar

PY - 2024

Y1 - 2024

N2 - We consider in parallel pointed homotopy automorphisms of iterated wedge sums of finite CW–complexes and boundary-relative homotopy automorphisms of iterated connected sums of manifolds minus a disk. Under certain conditions on the spaces and manifolds, we prove that the rational homotopy groups of these homotopy automorphisms form finitely generated FI–modules, and thus satisfy representation stability for symmetric groups in the sense of Church and Farb. We also calculate explicit bounds on the weights and stability degrees of these FI–modules.

AB - We consider in parallel pointed homotopy automorphisms of iterated wedge sums of finite CW–complexes and boundary-relative homotopy automorphisms of iterated connected sums of manifolds minus a disk. Under certain conditions on the spaces and manifolds, we prove that the rational homotopy groups of these homotopy automorphisms form finitely generated FI–modules, and thus satisfy representation stability for symmetric groups in the sense of Church and Farb. We also calculate explicit bounds on the weights and stability degrees of these FI–modules.

KW - homotopy automorphisms

KW - representation stability

U2 - 10.2140/agt.2024.24.2673

DO - 10.2140/agt.2024.24.2673

M3 - Journal article

AN - SCOPUS:85202822348

VL - 24

SP - 2673

EP - 2705

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 5

ER -

ID: 404229980