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- W4382765992 abstract "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." @default.
- W4382765992 created "2023-07-01" @default.
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- W4382765992 date "2023-06-29" @default.
- W4382765992 modified "2023-09-25" @default.
- W4382765992 title "On the cokernel of the Thom morphism for compact Lie groups" @default.
- W4382765992 doi "https://doi.org/10.48550/arxiv.2306.16874" @default.
- W4382765992 hasPublicationYear "2023" @default.
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