High-Dimensional Fillings in Heisenberg Groups

Robert Young

doi:10.1007/s12220-015-9601-y

High-Dimensional Fillings in Heisenberg Groups

Robert Young

Mathematics

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

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 language	English (US)
Pages (from-to)	1596-1616
Number of pages	21
Journal	Journal of Geometric Analysis
Volume	26
Issue number	2
DOIs	https://doi.org/10.1007/s12220-015-9601-y
State	Published - Apr 1 2016

Keywords

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

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-015-9601-y

Cite this

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keywords = "Carnot geometry, Dehn functions, Filling inequalities, Heisenberg group, Sub-Riemannian geometry",

author = "Robert Young",

note = "Funding Information: Parts of this paper were written at the Institut des Hautes {\'E}tudes Scientifiques and at New York University. The author was partially supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada and a grant from the Connaught Fund, University of Toronto. Publisher Copyright: {\textcopyright} 2015, Mathematica Josephina, Inc.",

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KW - Dehn functions

KW - Filling inequalities

KW - Heisenberg group

KW - Sub-Riemannian geometry

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High-Dimensional Fillings in Heisenberg Groups

Abstract

Keywords

ASJC Scopus subject areas

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