  We provide the complex Banach manifold structure for the Teichmueller space
of circle diffeomorphisms whose derivatives are in the Zygmund class. This is
done by showing that the Schwarzian derivative map is a holomorphic split
submersion. We prove similar results for the pre-Schwarzian derivative map and
investigate the fiber space over the Teichmueller space. Especially, we show
that this projection is also a holomorphic split submersion and induces the
structure of a disk bundle. Finally, we introduce the little Zygmund class and
consider the closed subspace given by this family of mappings in the
Teichmueller space.
