Hyperbolic Manifolds and Kleinian Groups

Diving into Hyperbolic Worlds: Manifolds and Kleinian Groups

A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, also seen as a subgroup of Möbius transformations in the complex plane. This book is a comprehensive guide to the theories of Kleinian groups from the perspectives of hyperbolic geometry and complex analysis.

After 1960, Ahlfors and Bers propelled Kleinian groups into an active area of complex analysis as a branch of Teichmüller th…