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Glasnik matematički, Vol. 56 No. 2, 2021.

Original scientific paper

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

On homotopy nilpotency

Marek Golasiński ; Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54 Street, 10-710 Olsztyn, Poland

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page 391-406

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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.

Keywords

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

Hrčak ID:

267561

URI

https://hrcak.srce.hr/267561

Publication date:

23.12.2021.

Visits: 391 *

Publication date: 31 December 2021

Volume: Vol 56

Issue: Svezak 2

Pages: 391-406

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

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: 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

On homotopy nilpotency

Marek Golasiński[1]

Email: marekg@matman.uwm.edu.pl

 

[1] Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54 Street, 10-710 Olsztyn, Poland

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.

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