Invariants of stably trivial vector bundles with connection
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866918148044750848 |
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| author | Moroianu, Sergiu |
| author_facet | Moroianu, Sergiu |
| contents | We define a Chern--Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in $3$-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for connections defined on a direct sum of bundles, under a certain block-diagonality condition on the curvature. As a corollary, we deduce an obstruction for conformally immersing a $n$-dimensional Riemannian manifold in a translation manifold of dimension $n+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invariants of stably trivial vector bundles with connection Moroianu, Sergiu Differential Geometry 58J28 We define a Chern--Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in $3$-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for connections defined on a direct sum of bundles, under a certain block-diagonality condition on the curvature. As a corollary, we deduce an obstruction for conformally immersing a $n$-dimensional Riemannian manifold in a translation manifold of dimension $n+1$. |
| title | Invariants of stably trivial vector bundles with connection |
| topic | Differential Geometry 58J28 |
| url | https://arxiv.org/abs/2509.21288 |