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 language | English (US) |
---|---|
Pages (from-to) | 41-108 |
Number of pages | 68 |
Journal | Duke Mathematical Journal |
Volume | 167 |
Issue number | 1 |
DOIs | |
State | Published - Jan 15 2018 |
Fingerprint
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
}
TY - JOUR
T1 - Quantitative nonorientability of embedded cycles
AU - Young, Robert
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.
UR - http://www.scopus.com/inward/record.url?scp=85042153044&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85042153044&partnerID=8YFLogxK
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 -