Invariants of stably trivial vector bundles with connection

Sergiu Moroianu

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arXiv · 2509.21288

Invariants of stably trivial vector bundles with connection

Sergiu Moroianu

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Abstract

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 $n+1$.

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Sergiu Moroianu. 2025-09-25. Invariants of stably trivial vector bundles with connection. https://arxiv.org/abs/2509.21288

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