Basic differential forms for actions of Lie groups

A section of a Riemannian $G$-manifold $M$ is a closed submanifold $\Sigma$ which meets each orbit orthogonally. It is shown that the algebra of $G$-invariant differential forms on $M$ which are horizontal in the sense that they kill every vector which is tangent to some orbit, is isomorphic to the algebra of those differential forms on $\Sigma$ which are invariant with respect to the generalized Weyl group of this orbit, under some condition.Comment: 10 pages, ESI Preprint 87, AmSTe

The homotopy type of the space of degree 0 immersed plane curves

The space of all immersed closed curves of rotation degree 0 in the plane modulo reparametrizations has the same homotopy groups as the circle times the 2-sphere.Comment: 7 page