A note on the Thom morphism for the classifying space of certain Lie groups and gauge groups

2024/05/21 by Kaspersen, Eiolf, Quick, Gereon
#55R35 #55S05 #55S10 #57R77 #57T10 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.12717

Abstract

We give a complete description of which non-torsion generators are not in the image of the Thom morphism from complex cobordism to integral cohomology for the classifying space of exceptional Lie groups except for E₈. We then show that the Thom morphism is not surjective for the classifying space of the gauge group of a principal E₇-bundle over the four-dimensional sphere. We use the results to detect nontrivial elements in the kernel of the reduced Thom morphism for Lie groups and their classifying spaces.

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