A note on Chern-Weil classes of Cartan connections
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915982316929024 |
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| author | Accornero, Luca de Melo, Mateus M. Struchiner, Ivan |
| author_facet | Accornero, Luca de Melo, Mateus M. Struchiner, Ivan |
| contents | We present a construction of Chern-Weil characteristic classes for pairs Cartan geometries sharing the same underlying data. Given any model Cartan geometry $(Q,ω)$ with underlying data $(G,V)$ and a second Cartan geometry $(P,θ)$ with the same underlying data, we define a subalgebra of polynomials on the Atiyah algebroid of $Q$ together with a characteristic map that recovers the classical Chern-Weil map of a Cartan connection when $(Q,ω)$ arises from a Klein pair modeling $(P,θ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on Chern-Weil classes of Cartan connections Accornero, Luca de Melo, Mateus M. Struchiner, Ivan Differential Geometry We present a construction of Chern-Weil characteristic classes for pairs Cartan geometries sharing the same underlying data. Given any model Cartan geometry $(Q,ω)$ with underlying data $(G,V)$ and a second Cartan geometry $(P,θ)$ with the same underlying data, we define a subalgebra of polynomials on the Atiyah algebroid of $Q$ together with a characteristic map that recovers the classical Chern-Weil map of a Cartan connection when $(Q,ω)$ arises from a Klein pair modeling $(P,θ)$. |
| title | A note on Chern-Weil classes of Cartan connections |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.00247 |