Parallelepipeds, Nilpotent Groups, and Gowers Norms

2006/05/31 by Host, Bernard, Kra, Bryna · 2 citations
#11B75 #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0606004

Abstract

In his proof of Szemeredi'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 3 and show when this possible, and describe a correspondence between the parallelepiped structures nilpotent groups.

Cited by

• An inverse theorem for all finite abelian groups via nilmanifolds
• Parseval-type identities for Gowers uniformity norms in finite abelian groups

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