Quantitative nonorientability of embedded cycles

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - Jan 15 2018

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Quantitative nonorientability of embedded cycles'. Together they form a unique fingerprint.

Cite this