TY - JOUR
T1 - Quantitative nonorientability of embedded cycles
AU - Young, Robert
N1 - Funding Information:
The author’s work was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada, by a grant from the Connaught Fund, University of Toronto, by a Sloan Research Fellowship, and by National Science Foundation grant DMS 1612061. Many of the theorems were proved while the author was employed at the University of Toronto.
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
VL - 167
SP - 41
EP - 108
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
SN - 0012-7094
IS - 1
ER -