TY - JOUR
T1 - Homotopy commutativity in Hermitian symmetric spaces
AU - Kishimoto, Daisuke
AU - Takeda, Masahiro
AU - Tong, Yichen
N1 - Funding Information:
The authors are grateful to Toshiyuki Miyauchi for informing them the result of Ōshima []. They are also grateful to the referee for improving the presentation of the paper. The authors were partially supported by JSPS KAKENHI Grant Number JP17K05248 and JP19K03473 (Kishimoto), JSPS KAKENHI Grant Number JP21J10117 (Takeda), and JST SPRING Grant Number JPMJSP2110 (Tong).
Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust.
PY - 2022
Y1 - 2022
N2 - Ganea proved that the loop space of ℂPn 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 ℂP3 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.
AB - Ganea proved that the loop space of ℂPn 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 ℂP3 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.
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U2 - 10.1017/S0017089522000118
DO - 10.1017/S0017089522000118
M3 - Article
AN - SCOPUS:85129853871
SN - 0017-0895
JO - Glasgow Mathematical Journal
JF - Glasgow Mathematical Journal
ER -