Homotopy classes of H-maps between Lie Groups

Abstract

In this thesis we study the homotopy classes of maps between two compact, simplyconnected, simple Lie groups G and L, with a view to classifying when all of these maps are homotopy equivalent to H-maps. We do this by studying the the homotopy classes of maps G → L, and the homotopy classes of H-maps G → L, as well as the homotopy classes of maps AG → L for a related space AG. By finding homotopy decompositions for these sets of classes, we may compare the decompositions, describe H[G, L], and give sufficient conditions for all maps G → L to be homotopy equivalent to H-maps. We extend this in some cases to give group isomorphisms between the groups of classes of maps. We draw together work by Theriault and Grbic on power maps and self maps of low ´ rank Lie groups, as well as work of Kishimoto and Kaji on homotopy nilpotency and older results of James, Cohen and Neisendorfer, and Mimura, Nishida and Toda

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ORCID for Stephen Theriault: orcid.org/0000-0002-7729-5527

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