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Self-Maps of Low Rank Lie Groups at Odd Primes

  Published:2009-12-04
 Printed: Apr 2010
  • Jelena Grbić
  • Stephen Theriault
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Abstract

Let G be a simple, compact, simply-connected Lie group localized at an odd prime~p. We study the group of homotopy classes of self-maps $[G,G]$ when the rank of G is low and in certain cases describe the set of homotopy classes of multiplicative self-maps $H[G,G]$. The low rank condition gives G certain structural properties which make calculations accessible. Several examples and applications are given.
Keywords: Lie group, self-map, H-map Lie group, self-map, H-map
MSC Classifications: 55P45, 55Q05, 57T20 show english descriptions $H$-spaces and duals
Homotopy groups, general; sets of homotopy classes
Homotopy groups of topological groups and homogeneous spaces
55P45 - $H$-spaces and duals
55Q05 - Homotopy groups, general; sets of homotopy classes
57T20 - Homotopy groups of topological groups and homogeneous spaces
 

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