Homotopy commutativity in symmetric spaces

We extend previous results of Ganea and the two of the authors with Takeda on the homotopy commutativity of the loop spaces of Hermitian symmetric spaces to show that the loop spaces of all irreducible symmetric spaces but C P 3 are not homotopy commutative.

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Bibliographic Details
Published inBoletín de la Sociedad Matemática Mexicana Vol. 30; no. 2
Main Authors Kishimoto, Daisuke, Minowa, Yuki, Miyauchi, Toshiyuki, Tong, Yichen
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.07.2024
Springer Nature B.V
Subjects
Commutativity
Mathematics
Mathematics and Statistics
Original Article
Generalized Whitehead product
55Q15
Samelson product
Homotopy commutativity
Symmetric space
55P35
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Summary:We extend previous results of Ganea and the two of the authors with Takeda on the homotopy commutativity of the loop spaces of Hermitian symmetric spaces to show that the loop spaces of all irreducible symmetric spaces but C P 3 are not homotopy commutative.
ISSN:1405-213X
2296-4495
DOI:10.1007/s40590-024-00616-5