Glasnik Matematicki, Vol. 56, No. 2 (2021), 391-406. \( \)

ON HOMOTOPY NILPOTENCY

Marek Golasiński

Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54 Street, 10-710 Olsztyn, Poland
e-mail:marekg@matman.uwm.edu.pl

Abstract.   We review established and recent results on the homotopy nilpotence of spaces. In particular, the homotopy nilpotency of the loop spaces \(\Omega(G/K)\) of homogenous spaces \(G/K\) for a compact Lie group \(G\) and its closed homotopy nilpotent subgroup \(K \lt G\) is discussed.

2020 Mathematics Subject Classification.   55P15, 20F18, 55P35, 55P60.

Key words and phrases.   Classical Lie group, co-category, flag manifold, (oriented) flat product, (oriented) Grassmann manifold, homogeneous space, nilpotency class, \(H\)-fibration, \(n\)-fold commutator map, \(H\)-space, loop space, Morava \(K\)-theory, \(p\)-localization, Postnikov system, projective space, sphere, Stiefel manifold, suspension space, smash product

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https://doi.org/10.3336/gm.56.2.10

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