Parallelepipeds, nilpotent groups and Gowers norms

Bernard Host; Bryna Kra

doi:10.24033/bsmf.2561

Parallelepipeds, nilpotent groups and Gowers norms

Bernard Host^*, Bryna Kra

^*Corresponding author for this work

Mathematics

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

22 Scopus citations

Abstract

In his proof of Szemerédi's Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers norm) can be defined. We focus on dimensions ² and ³and show when this possible, and describe a correspondence between the parallelepiped structures and nilpotent groups.

Original language	English (US)
Pages (from-to)	405-437
Number of pages	33
Journal	Bulletin de la Societe Mathematique de France
Volume	136
Issue number	3
DOIs	https://doi.org/10.24033/bsmf.2561
State	Published - 2008

Funding

Keywords

Gowers norms
Nilpotent group
Parallelepiped

ASJC Scopus subject areas

General Mathematics

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10.24033/bsmf.2561

Cite this

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abstract = "In his proof of Szemer{\'e}di's Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers norm) can be defined. We focus on dimensions 2 and 3and show when this possible, and describe a correspondence between the parallelepiped structures and nilpotent groups.",

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AB - In his proof of Szemerédi's Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers norm) can be defined. We focus on dimensions 2 and 3and show when this possible, and describe a correspondence between the parallelepiped structures and nilpotent groups.

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KW - Nilpotent group

KW - Parallelepiped

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Parallelepipeds, nilpotent groups and Gowers norms

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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