Article contents
Homotopy commutativity in Hermitian symmetric spaces
Published online by Cambridge University Press: 18 April 2022
Abstract
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.
MSC classification
- Type
- Research Article
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- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust
References
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