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Classes Minimales de Réseaux et Rétractions Géométriques Équivariantes Dans Les Espaces Symétriques
Author(s) -
Bavard Christophe
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610701002319
Subject(s) - equivariant map , mathematics , pure mathematics , symmetric space , space (punctuation) , euclidean space , codimension , mathematical analysis , combinatorics , philosophy , linguistics
Equivariant and cocompact retractions of certain symmetric spaces are constructed. These retractions are defined using the natural geometry of symmetric spaces and in relation to the theory of lattices of euclidean space. The following cases are considered: the symmetric space corresponding to lattices endowed with a finite group action, from which is obtained some information relating to the classification problem of these lattices, and the Siegel space Sp 2 g ( R )/ U g , for which a natural Sp 2 g ( Z )‐equivariant cocompact retract of codimension 1 is obtained.