The group of homotopy equivalences of products of spheres and of Lie groups |
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Authors: | Martin Arkowitz Jeffrey Strom |
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Affiliation: | (1) Dartmouth College, Hanover, NH 03755, USA (e-mail: {martin.arkowitz,jeffrey.strom}@dartmouth.edu) , US |
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Abstract: | We investigate the group of self homotopy equivalences of a space X which induce the identity homomorphism on all homotopy groups. We obtain results on the structure of provided the p-localization of X has the homotopy type of a p-local product of odd-dimensional spheres. In particular, we show that is a semidirect product of certain homotopy groups . We also show that has a central series whose successive quotients are , which are direct sums of homotopy groups of p-local spheres. This leads to a determination of the order of the p-torsion subgroup of and an upper bound for its p-exponent. These results apply to any Lie group G at a regular prime p. We derive some general properties of and give numerous explicit calculations. Received: 14 April 2001; in final form: 10 September 2001 / Published online: 17 June 2002 |
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Keywords: | Mathematics Subject Classification (1991): 55P10 55P60 55S37 |
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