J. Math. Sci. Univ. Tokyo
Vol. 7 (2000), No. 3, Page 487--508.

GusmÃ£o, Paulo

Abstract:
Let us consider non transversaly orientable measurable foliations of codimension one, on orientable open manifolds $M^n$, $n\ge 3$. We calculated the subgroups of finite type of two groups: one is the fundamental group $Î _1(BÎ)$ of the Haefliger's classifying space and the other is the quotient of $Î _1(M)$ by the normal subgroup ${\Cal L}'$ generated by free homotopy classes of the loops contained in the leaves. We use these groups to extend the result of G. Levitt to a no-orientable case. This result caracterize the finite type groups acting freely on a simply connected 1-manifold by $C^2$-diffeomorphism which preserves orientation. We study the pseudogroups of the isometries of the circle and we calculated the variation of the measure of the orbite space when we modified the length of the domain of the generators.

Mathematics Subject Classification (1991): 58H05, 57R30, 58F18
Mathematical Reviews Number: MR1792738