Determination of the multiplicative nilpotency of self-homotopy sets

zbMATH Open1120.55010arXiv0903.4607MaRDI QIDQ3419527

Ken-ichi Maruyama

Publication date: 6 February 2007

Abstract: The semigroup of the homotopy classes of the self-homotopy maps of a finite complex which induce the trivial homomorphism on homotopy groups is nilpotent. We determine the nilpotency of these semigroups of compact Lie groups and finite Hopf spaces of rank 2. We also study the nilpotency of semigroups for Lie groups of higher rank. Especially, we give Lie groups with the nilpotency of the semigroups arbitrarily large.

Full work available at URL: https://arxiv.org/abs/0903.4607

zbMATH Keywords

Lie groupslocalisation\(H\)-spacesnilpotency

Mathematics Subject Classification ID

(H)-spaces and duals (55P45) Homotopy groups, general; sets of homotopy classes (55Q05) Localization and completion in homotopy theory (55P60) Finite nilpotent groups, (p)-groups (20D15) Whitehead products and generalizations (55Q15)

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