arXiv subjects

Eiolf Kaspersen

Publications and source records attributed to Eiolf Kaspersen.

3 recordsLinked to original sources

arXiv2024

Geometric representation of cohomology classes for the Lie groups Spin(7) and Spin(8)

By constructing concrete complex-oriented maps we show that the eight-fold of the generator of the third integral cohomology of the spin groups Spin(7) and Spin(8) is in the image of the Thom morphism from complex cobordism to singular cohomology, while the generator itself is not in the image. We thereby give a geometric construction for a nontrivial class in the kernel of the differential Thom morphism of Hopkins and Singer for the Lie groups Spin(7) and Spin(8). The construction exploits the special symmetries of the octonions.

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arXiv2024

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

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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arXiv2023

On the cokernel of the Thom morphism for compact Lie groups

We give a complete description of the potential failure of the surjectivity of the Thom morphism from complex cobordism to integral cohomology for compact Lie groups via a detailed study of the Atiyah-Hirzebruch spectral sequence and the action of the Steenrod algebra. We show how the failure of the surjectivity of the topological Thom morphism can be used to find examples of non-trivial elements in the kernel of the induced differential Thom morphism from differential cobordism of Hopkins and Singer to differential cohomology. These arguments are based on the particular algebraic structure and interplay of the torsion and non-torsion parts of the cohomology and cobordism rings of a given compact Lie group. We then use the geometry of special orthogonal groups to construct concrete cobordism classes in the non-trivial part of the kernel of the differential Thom morphism.

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