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Determination of the multiplicative nilpotency of
self-homotopy sets
Ken-ichi Maruyama
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Geometry & Topology Monographs 10
(2007) 281–292
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Abstract
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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.
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Keywords
self-homotopy sets, Lie groups,
H–spaces
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Mathematical Subject Classification
Primary: 55P10, 55Q05, 57T20
Secondary: 20D15, 55P60
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Publication
Received: 13 August 2004
Revised: 22 June 2005
Published: 29 January 2007
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