LUSTERNIK-SCHNIRELMANN CATEGORY AND ALGEBRAIC R-LOCAL HOMOTOPY-THEORY

In this paper, we define the notion of R-LS category associated to an increasing system of subrings of Q and we relate it to the usual LS-c ategory. We also relate it to the invariant introduced by Felix and Le maire in tame homotopy theory, in which case we give a description in terms of Lie algebras and of cocommutative coalgebras, extending resul ts of Lemaire-Sigrist and Felix-Halperin.