TY - JOUR
T1 - Quantitative nonorientability of embedded cycles
AU - Young, Robert
N1 - Publisher Copyright:
© 2018 Duke Mathematical Journal.
PY - 2018/1/15
Y1 - 2018/1/15
N2 - 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.
AB - 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.
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U2 - 10.1215/00127094-2017-0035
DO - 10.1215/00127094-2017-0035
M3 - Article
AN - SCOPUS:85042153044
SN - 0012-7094
VL - 167
SP - 41
EP - 108
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 1
ER -