Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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A survey of homotopy nilpotency and co-nilpotency

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Published Oct 13, 2020
DOI https://doi.org/10.15673/tmgc.v13i4.1750

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Marek Golasinski
University of Warmia and Mazury
http://orcid.org/0000-0001-6969-8986

Abstract

We review known and state some new results on homotopy nilpotency and co-nilpotency of spaces. Next, we take up the systematic study of homotopy nilpotency of homogenous spaces G/K for a Lie group G and its closed subgroup K < G. The homotopy nilpotency of the loop spaces Ω(Gn,m(K)) and Ω(Vn,m(K)) of Grassmann Gn,m(K) and Stiefel Vn,m(K) manifolds for K = R, C, the field of reals or complex numbers and H, the skew R-algebra of quaternions is shown.

Keywords:
classical Lie group, H -fibration, flag manifold, (oriented) Grassmann manifold, homogenous space, homology decomposition, homotopy nilpotency (co-nilpotency) class, H -space, H0-space, n-fold commutator (co-commutator) map, p-localization, loop space, Morava K-theory, Postnikov system, projective space, sphere, Stiefel manifold, suspension space, smash product

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How to Cite
Golasinski, M. (2020). A survey of homotopy nilpotency and co-nilpotency. Proceedings of the International Geometry Center, 13(4), 1-23. https://doi.org/10.15673/tmgc.v13i4.1750
Issue
Vol 13 No 4 (2020): A special issue devoted to V.V.Sharko
Section
Papers

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Author Biography

Marek Golasinski, University of Warmia and Mazury

Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Sloneczna 54 Street, 10-710 Olsztyn, Poland