Intrinsic flat convergence of covering spaces

Zahra Sinaei, Christina Sormani*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We examine the limits of covering spaces and the covering spectra of oriented Riemannian manifolds, Mj, which converge to a nonzero integral current space, M, 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 Mj diffeomorphic to S4 that converge in the intrinsic flat sense to a torus S1× S3. Nevertheless, we prove that if the δ-covers, M~jδ, have finite order N, then a subsequence of the M~jδ converge in the intrinsic flat sense to a metric space, M∞δ, which is the disjoint union of covering spaces of M.

Original languageEnglish (US)
Pages (from-to)83-114
Number of pages32
JournalGeometriae Dedicata
Volume184
Issue number1
DOIs
StatePublished - Oct 1 2016

Keywords

  • Covering space
  • Covering spectra
  • Intrinsic flat convergence

ASJC Scopus subject areas

  • Geometry and Topology

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