Schützenberger groups of some even degree polynomials in S(R).
We study the cohomology of the group consisting of all -diffeomorphisms of the line, which are -flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group.
We prove that the space of orientation preserving homeomorphisms of the 2-sphere which fix pointwise a nontrivial nonseparating continuum is a contractible absolute neighborhood retract homeomorphic to the separable Hilbert space .