A nonlocal approximation of the area in codimension two

For $s\in (0,1)$ we introduce a notion of fractional $s$-mass on $(n-2)$-dimensional closed, orientable surfaces in ${\mathbb{R}}^n$. Moreover, we prove its $\mathrm{\Gamma }$-convergence, with respect to the flat topology, and pointwise convergence to the $(n-2)$-dimensional area.