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Alexandrov Spaces with Integral Current Structure

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Catherine Searle
Wichita State University
Thu, 2017-07-20 16:30 - 17:30
MPIM Lecture Hall

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.


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