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arXiv · 2405.12717

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

Eiolf Kaspersen·Gereon Quick
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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 E_8. We then show that the Thom morphism is not surjective for the classifying space of the gauge group of a principal E_7-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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Eiolf Kaspersen, Gereon Quick. 2024-05-21. A note on the Thom morphism for the classifying space of certain Lie groups and gauge groups. https://arxiv.org/abs/2405.12717

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