High-Dimensional Fillings in Heisenberg Groups

Research output: Contribution to journalArticle

Abstract

We use intersections with horizontal manifolds to show that high-dimensional cycles in the Heisenberg group can be approximated efficiently by simplicial cycles. This lets us calculate all of the higher-order Dehn functions of the Heisenberg groups, thus proving a conjecture of Gromov.

Original languageEnglish (US)
Pages (from-to)1596-1616
Number of pages21
JournalJournal of Geometric Analysis
Volume26
Issue number2
DOIs
StatePublished - Apr 1 2016

Fingerprint

Heisenberg Group
High-dimensional
Dehn Function
Cycle
Horizontal
Intersection
Higher Order
Calculate

Keywords

  • Carnot geometry
  • Dehn functions
  • Filling inequalities
  • Heisenberg group
  • Sub-Riemannian geometry

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

High-Dimensional Fillings in Heisenberg Groups. / Young, Robert.

In: Journal of Geometric Analysis, Vol. 26, No. 2, 01.04.2016, p. 1596-1616.

Research output: Contribution to journalArticle

@article{b128ce4eba774c03b21c56b525f0b6d5,
title = "High-Dimensional Fillings in Heisenberg Groups",
abstract = "We use intersections with horizontal manifolds to show that high-dimensional cycles in the Heisenberg group can be approximated efficiently by simplicial cycles. This lets us calculate all of the higher-order Dehn functions of the Heisenberg groups, thus proving a conjecture of Gromov.",
keywords = "Carnot geometry, Dehn functions, Filling inequalities, Heisenberg group, Sub-Riemannian geometry",
author = "Robert Young",
year = "2016",
month = "4",
day = "1",
doi = "10.1007/s12220-015-9601-y",
language = "English (US)",
volume = "26",
pages = "1596--1616",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "Springer New York",
number = "2",

}

TY - JOUR

T1 - High-Dimensional Fillings in Heisenberg Groups

AU - Young, Robert

PY - 2016/4/1

Y1 - 2016/4/1

N2 - We use intersections with horizontal manifolds to show that high-dimensional cycles in the Heisenberg group can be approximated efficiently by simplicial cycles. This lets us calculate all of the higher-order Dehn functions of the Heisenberg groups, thus proving a conjecture of Gromov.

AB - We use intersections with horizontal manifolds to show that high-dimensional cycles in the Heisenberg group can be approximated efficiently by simplicial cycles. This lets us calculate all of the higher-order Dehn functions of the Heisenberg groups, thus proving a conjecture of Gromov.

KW - Carnot geometry

KW - Dehn functions

KW - Filling inequalities

KW - Heisenberg group

KW - Sub-Riemannian geometry

UR - http://www.scopus.com/inward/record.url?scp=84961063224&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961063224&partnerID=8YFLogxK

U2 - 10.1007/s12220-015-9601-y

DO - 10.1007/s12220-015-9601-y

M3 - Article

AN - SCOPUS:84961063224

VL - 26

SP - 1596

EP - 1616

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

IS - 2

ER -