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15 January 2018 Quantitative nonorientability of embedded cycles
Robert Young
Duke Math. J. 167(1): 41-108 (15 January 2018). DOI: 10.1215/00127094-2017-0035

Abstract

We introduce an invariant linked to some foundational questions in geometric measure theory and provide bounds on this invariant by decomposing an arbitrary cycle into uniformly rectifiable pieces. Our invariant measures the difficulty of cutting a nonorientable closed manifold or mod-2 cycle in Rn into orientable pieces, and we use it to answer some simple but long-open questions on filling volumes and mod-ν currents.

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Robert Young. "Quantitative nonorientability of embedded cycles." Duke Math. J. 167 (1) 41 - 108, 15 January 2018. https://doi.org/10.1215/00127094-2017-0035

Information

Received: 28 January 2016; Revised: 9 May 2017; Published: 15 January 2018
First available in Project Euclid: 15 November 2017

zbMATH: 06847242
MathSciNet: MR3743699
Digital Object Identifier: 10.1215/00127094-2017-0035

Subjects:
Primary: 49Q15
Secondary: 53A07

Keywords: filling volume , integral currents , orientability , uniform rectifiability

Rights: Copyright © 2018 Duke University Press

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Vol.167 • No. 1 • 15 January 2018
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