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- W2952479072 abstract "We examine the limits of covering spaces and the covering spectra of oriented Riemannian manifolds, $M_j$, which converge to a nonzero integral current space, $M_infty$, in the intrinsic flat sense. We provide examples demonstrating that the covering spaces and covering spectra need not converge in this setting. In fact we provide a sequence of simply connected $M_j$ diffeomorphic to $mathbb{S}^4$ that converge in the intrinsic flat sense to a torus $mathbb{S}^1timesmathbb{S}^3$. Nevertheless, we prove that if the $delta$-covers, $tilde{M}_j^delta$, have finite order $N$, then a subsequence of the $tilde{M}_j^delta$ converge in the intrinsic flat sense to a metric space, $M^delta_infty$, which is the disjoint union of covering spaces of $M_infty$." @default.
- W2952479072 created "2019-06-27" @default.
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- W2952479072 date "2014-09-24" @default.
- W2952479072 modified "2023-09-27" @default.
- W2952479072 title "Intrinsic Flat Convergence of Covering Spaces" @default.
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