Actions of groups of foliated homeomorphisms on spaces of leaves

Abstract

Let ∆ be a foliation on a topological manifold X, Y be the space of leaves, and p : X → Y be the natural projection. Endow Y with the factor topology with respect to p. Then the group H(X, ∆) of foliated (i.e. mapping leaves onto leaves) homeomorphisms of X naturally acts on the space of leaves Y , which gives a homomorphism ψ : H(X, ∆) → H(Y ). We present sufficient conditions when ψ is continuous with respect to the corresponding compact open topologies.In fact similar results hold not only for foliations but for a more general class of partitions ∆ of locally compact Hausdorff spaces X.

Yamabe problem in the presence of singular Riemannian Foliations

“…To conclude this section, let us recall some results on foliated homeomorphisms (cf. [32,Section 3]). Let p : X → Y be a quotient map between two topological spaces X and Y .…”