We endow each closed, orientable Alexandrov space $(X,d)$ with an integral current $T$ of weight equal to 1,
$\partial T = 0$ and $\mbox{set}(T)=X$ , in other words, we prove that $(X,d,T)$ is an integral current spacewith no boundary.
Combining this result with a result of Li and Perales, we show that non-collapsing sequences of these spaces with uniform lower curvature and diameter bounds admit subsequences whose Gromov-Hausdorff and intrinsic flat limits agree.
This is joint work with Maree Jaramillo, Raquel Perales, Priyanka Rajan and Anna Siffert.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/3050