This paper aims to define and study currents and slices of currents in the Heisenberg group \({\mathbb {H}}^n\). Currents, depending on their integration properties and on those of their boundaries, can be classified into subspaces and, assuming their support to be compact, we can work with currents of finite mass, define the notion of slices of Heisenberg currents and show some important properties for them. While some such properties are similarly true in Riemannian settings, others carry deep consequences because they do not include the slices of the middle dimension n, which opens new challenges and scenarios for the possibility of developing a compactness theorem. Furthermore, this suggests that the study of currents on the first Heisenberg group \({\mathbb {H}}^1\) diverges from the other cases, because that is the only situation in which the dimension of the slice of a hypersurface, \(2n-1\), coincides with the middle dimension n, which triggers a change in the associated differential operator in the Rumin complex.

本文旨在定义和研究Heisenberg组\（{\ mathbb {H}} ^ n \）中的电流和电流切片。根据积分性质及其边界性质，可以将电流分类为子空间，并且假设它们的支持是紧凑的，我们可以使用有限质量的电流，定义海森堡电流的切片概念并显示一些重要的性质为他们。尽管某些此类特性在黎曼环境中同样适用，但其他特性却产生了深远的影响，因为它们不包括中间维n的切片，这为开发紧性定理的可能性带来了新的挑战和情况。此外，这表明对第一个海森堡群\（{\ mathbb {H}} ^ 1 \）上的电流的研究与其他情况不同，因为那是唯一的情况，其中超曲面的切片\\（2n-1 \）的尺寸与中间尺寸n一致，从而触发了Rumin中相关的微分算子的变化复杂。