Quantitative nonorientability of embedded cycles

Robert Young

Research output: Contribution to journal › Article

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-v currents.

Original languageEnglish (US)
Pages (from-to)41-108
Number of pages68
JournalDuke Mathematical Journal
Volume167
Issue number1
DOIs
StatePublished - Jan 15 2018

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Geometric Measure Theory
Cycle
Invariant
Invariant Measure
Closed
Arbitrary

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Quantitative nonorientability of embedded cycles. / Young, Robert.

In: Duke Mathematical Journal, Vol. 167, No. 1, 15.01.2018, p. 41-108.

Research output: Contribution to journal › Article

Young, R 2018, 'Quantitative nonorientability of embedded cycles', Duke Mathematical Journal, vol. 167, no. 1, pp. 41-108. https://doi.org/10.1215/00127094-2017-0035
Young R. Quantitative nonorientability of embedded cycles. Duke Mathematical Journal. 2018 Jan 15;167(1):41-108. https://doi.org/10.1215/00127094-2017-0035
Young, Robert. / Quantitative nonorientability of embedded cycles. In: Duke Mathematical Journal. 2018 ; Vol. 167, No. 1. pp. 41-108.
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