$λ$-ring structure in differential K-theory
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917244621029376 |
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| author | Liu, Bo Ma, Xiaonan |
| author_facet | Liu, Bo Ma, Xiaonan |
| contents | We establish the splitting principle for differential K-theory, a refinement of topological K-theory that incorporates geometric data via differential forms. Using this principle, we prove that the differential $K^0$-ring associated to closed smooth manifolds admits a $λ$-ring structure. This structure enables a concrete construction of the Adams operations in differential K-theory introduced by Bunke. At last, we extend all these results to an equivariant setting associated with a compact Lie group action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03450 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $λ$-ring structure in differential K-theory Liu, Bo Ma, Xiaonan K-Theory and Homology Differential Geometry 19L50, 19L20, 19L47 We establish the splitting principle for differential K-theory, a refinement of topological K-theory that incorporates geometric data via differential forms. Using this principle, we prove that the differential $K^0$-ring associated to closed smooth manifolds admits a $λ$-ring structure. This structure enables a concrete construction of the Adams operations in differential K-theory introduced by Bunke. At last, we extend all these results to an equivariant setting associated with a compact Lie group action. |
| title | $λ$-ring structure in differential K-theory |
| topic | K-Theory and Homology Differential Geometry 19L50, 19L20, 19L47 |
| url | https://arxiv.org/abs/2602.03450 |