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In this paper we establish weak continuity results for the distributionJacobian minors in fractional sobolev spaces, which can be seen as a extensionof recent work of Brezis and Nguyen on the distributional Jacobian determinant.Then we apply results to introduce the currents associated with graphs of mapsin fractional Sobolev spaces and study some relevant properties such asstructure properties, weak continuity and so on. As another application, weextend the definition of functions of bounded higher variation, which definedby Jerrard and Soner in $W^{1,N-1}\cap L^{\infty}(\Omega,\mathbb{R}^N)$ ($\mbox{dim}\Omega\geq N$), to $W^{1-\frac{1}{N},N}(\Omega,\mathbb{R}^N)$ andgive some results including weak coarea formula, strong coarea formula andchain rule.

Cartesian currents in fractional Sobolev spaces and applications to functions of bounded higher variation