Homotopy commutativity in Hermitian symmetric spaces
Glasgow mathematical journal, Tome 64 (2022) no. 3, pp. 746-752
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Ganea proved that the loop space of $\mathbb{C} P^n$ is homotopy commutative if and only if $n=3$. We generalize this result to that the loop spaces of all irreducible Hermitian symmetric spaces but $\mathbb{C} P^3$ are not homotopy commutative. The computation also applies to determining the homotopy nilpotency class of the loop spaces of generalized flag manifolds $G/T$ for a maximal torus T of a compact, connected Lie group G.
Kishimoto, Daisuke; Takeda, Masahiro; Tong, Yichen. Homotopy commutativity in Hermitian symmetric spaces. Glasgow mathematical journal, Tome 64 (2022) no. 3, pp. 746-752. doi: 10.1017/S0017089522000118
@article{10_1017_S0017089522000118,
author = {Kishimoto, Daisuke and Takeda, Masahiro and Tong, Yichen},
title = {Homotopy commutativity in {Hermitian} symmetric spaces},
journal = {Glasgow mathematical journal},
pages = {746--752},
year = {2022},
volume = {64},
number = {3},
doi = {10.1017/S0017089522000118},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089522000118/}
}
TY - JOUR AU - Kishimoto, Daisuke AU - Takeda, Masahiro AU - Tong, Yichen TI - Homotopy commutativity in Hermitian symmetric spaces JO - Glasgow mathematical journal PY - 2022 SP - 746 EP - 752 VL - 64 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089522000118/ DO - 10.1017/S0017089522000118 ID - 10_1017_S0017089522000118 ER -
%0 Journal Article %A Kishimoto, Daisuke %A Takeda, Masahiro %A Tong, Yichen %T Homotopy commutativity in Hermitian symmetric spaces %J Glasgow mathematical journal %D 2022 %P 746-752 %V 64 %N 3 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089522000118/ %R 10.1017/S0017089522000118 %F 10_1017_S0017089522000118
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