Lusternik-Schnirelmann category and algebraic $R$-local homotopy theory

http://dx.doi.org/10.4153/CJM-1998-045-4
Canad. J. Math. 50(1998), 845-862

  Published:1998-08-01
 Printed: Aug 1998

In this paper, we define the notion of $R_{\ast}$-$\LS$ category associated to an increasing system of subrings of $\Q$ and we relate it to the usual $\LS$-category. We also relate it to the invariant introduced by F\'elix and Lemaire in tame homotopy theory, in which case we give a description in terms of Lie algebras and of cocommutative coalgebras, extending results of Lemaire-Sigrist and F\'elix-Halperin.