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PARALLELEPIPEDS, NILPOTENT GROUPS AND GOWERS NORMS

Abstract : 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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693082
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Submitted on : Tuesday, May 1, 2012 - 8:01:11 PM
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  • HAL Id : hal-00693082, version 1

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Bernard Host, Bryna Kra. PARALLELEPIPEDS, NILPOTENT GROUPS AND GOWERS NORMS. Bulletin de la société mathématique de France, Société Mathématique de France, 2008, 136 (3), pp.405--437. ⟨hal-00693082⟩

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