Determination of the multiplicative nilpotency of self-homotopy sets

Details Determination of the multiplicative nilpotency of self-homotopy sets Determination of the multiplicative nilpotency of self-homotopy sets

2009-03-26

arxiv.org/abs/0903.4607v1

Geom. Topol. Monogr. 10 (2007) 281-292

Mathematics

Algebraic Topology

This is the version published by Geometry & Topology Monographs on 29 January 2007

Scientific paper

10.2140/gtm.2007.10.281

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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