Representation stability for homotopy automorphisms
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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
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TY - JOUR
T1 - Representation stability for homotopy automorphisms
AU - Lindell, Erik
AU - Saleh, Bashar
N1 - Publisher Copyright: © 2024 MSP (Mathematical Sciences Publishers).
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