On perfection relations in lattices
Anne-Marie Bergé, Jacques Martinet · Contemporary mathematics - American Mathematical Society · 2009
Abstract. Let Λ 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 Λ. 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, Ryˇskov, Zahareva and the second author in [W], [R], [Z] and [M1]. 1.