Weil-Petersson Metric on the Universal Teichmuller Space

Proves that the universal Teichmuller space $T(1)$ carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of $T(1)$ - the Hilbert submanifold $T_{0}(1)$ - is a topological group. This book defines Weil-Petersson metric on $T(1)$ by Hilbert space inner products on tangent spaces.