Volumes, middle-dimensional systoles, and whitehead products

Ivan K. Babenko; Mikhail G. Katz; Alexander I. Suciu

doi:10.4310/MRL.1998.v5.n4.a4

Volumes, middle-dimensional systoles, and whitehead products

Ivan K. Babenko, Mikhail G. Katz, Alexander I. Suciu

Research output: Contribution to journal › Article › peer-review

Abstract

Let X be a closed, orientable, smooth manifold of dimension 2m ≥ 6 with torsion-free middle-dimensional homology. We construct metrics on X of arbitrarily small volume, such that every orientable, middle-dimensional submanifold of less than unit volume necessarily bounds. Thus, Loewner's theorem has no higher-dimensional analogue.

Original language	English
Pages (from-to)	461-471
Number of pages	11
Journal	Mathematical Research Letters
Volume	5
Issue number	4
DOIs	https://doi.org/10.4310/MRL.1998.v5.n4.a4
State	Published - 1998
Externally published	Yes

Keywords

Coarea inequality
Hilton-Milnor theorem
Isoperimetric inequality
Systole
Systolic freedom
Volume
Whitehead product

Access to Document

10.4310/MRL.1998.v5.n4.a4

Cite this

@article{a88aee9f0ca6479b87ce35c97514e899,

title = "Volumes, middle-dimensional systoles, and whitehead products",

abstract = "Let X be a closed, orientable, smooth manifold of dimension 2m ≥ 6 with torsion-free middle-dimensional homology. We construct metrics on X of arbitrarily small volume, such that every orientable, middle-dimensional submanifold of less than unit volume necessarily bounds. Thus, Loewner's theorem has no higher-dimensional analogue.",

keywords = "Coarea inequality, Hilton-Milnor theorem, Isoperimetric inequality, Systole, Systolic freedom, Volume, Whitehead product",

author = "Babenko, {Ivan K.} and Katz, {Mikhail G.} and Suciu, {Alexander I.}",

year = "1998",

doi = "10.4310/MRL.1998.v5.n4.a4",

language = "אנגלית",

volume = "5",

pages = "461--471",

journal = "Mathematical Research Letters",

issn = "1073-2780",

publisher = "International Press of Boston, Inc.",

number = "4",

}

TY - JOUR

T1 - Volumes, middle-dimensional systoles, and whitehead products

AU - Babenko, Ivan K.

AU - Katz, Mikhail G.

AU - Suciu, Alexander I.

PY - 1998

Y1 - 1998

N2 - Let X be a closed, orientable, smooth manifold of dimension 2m ≥ 6 with torsion-free middle-dimensional homology. We construct metrics on X of arbitrarily small volume, such that every orientable, middle-dimensional submanifold of less than unit volume necessarily bounds. Thus, Loewner's theorem has no higher-dimensional analogue.

AB - Let X be a closed, orientable, smooth manifold of dimension 2m ≥ 6 with torsion-free middle-dimensional homology. We construct metrics on X of arbitrarily small volume, such that every orientable, middle-dimensional submanifold of less than unit volume necessarily bounds. Thus, Loewner's theorem has no higher-dimensional analogue.

KW - Coarea inequality

KW - Hilton-Milnor theorem

KW - Isoperimetric inequality

KW - Systole

KW - Systolic freedom

KW - Volume

KW - Whitehead product

UR - http://www.scopus.com/inward/record.url?scp=0032219338&partnerID=8YFLogxK

U2 - 10.4310/MRL.1998.v5.n4.a4

DO - 10.4310/MRL.1998.v5.n4.a4

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0032219338

SN - 1073-2780

VL - 5

SP - 461

EP - 471

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 4

ER -

Volumes, middle-dimensional systoles, and whitehead products

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this