On Perfection Relations in Lattices

2006/11/08 by Anne-Marie Bergé Jacques Martinet, Martinet, Anne-Marie Bergé Jacques
Mathematics · #11H55 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT #msc:11H55

paper · pdf · doi:10.48550/arxiv.math/0611220

26 pages

arxiv created 2006/11/08 · openalex publication_date 2006/11/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \Lb be a lattice in a Euclidean space E, with kissing number s and perfection rank r, that is, the rank in \End^sym(E) of the set of orthogonal projections to minimal vectors of \Lb. This defines a space of perfection relations, of dimension s-r. We focus on ``short relations'', in connection with the index theory, previously developed by Watson, Ryškov, Zahareva and the second author in [W], [R], [Z] and [M1].

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