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