Parallelepipeds, nilpotent groups and Gowers norms

Bernard Host*, Bryna Kra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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 languageEnglish (US)
Pages (from-to)405-437
Number of pages33
JournalBulletin de la Societe Mathematique de France
Issue number3
StatePublished - 2008


  • Gowers norms
  • Nilpotent group
  • Parallelepiped

ASJC Scopus subject areas

  • Mathematics(all)

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