A note on the Thom morphism for the classifying space of certain Lie groups and gauge groups
Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Kaspersen, Eiolf, Quick, Gereon
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Norges Forskningsråd
OpenAlex ID: W4398230685