Teichmller Theory And Applications To Geometry Topology And Dynamics Volume 3 Manifolds That Fiber Over The Circle John Hamal Hubbard by John Hamal Hubbard 9781943863013, 1943863016 instant download after payment.

The first chapter concerns hyperbolic geometry and Kleinian groups. Topics include Jørgensen's inequality, the Margulis lemma, algebraic and especially geometric limits with both the Chabauty and the Thurston-Gromov approaches, the Klein-Maskit combination theorems, the Poincaré polyhedron theorem, and geometrically finite Kleinian groups.

The second chapter covers rigidity theorems: Ahlfors, McMullen, and Mostow. Verifying that quasi-Fuchsian groups satisfy the hypothesis of the McMullen rigidity theorem is a long and beautiful trip through laminations and pleated surfaces.

The third chapter proves the main result, visiting on the way the compactness of Bers slices, R-trees, Chiswell functions, Hatcher's construction and Skora's theorem, and the Otal compactness theorem.

The appendices take up 200 pages. Topics include the Nullstellensatz and Selberg's lemma, the relation between the ideal class group and the ends of Bianchi manifolds, the Haudorff dimension (1) of the space of simple geodesics on a hyperbolic surface, period coordinates, the ergodic theorem and Hopf's argument, the volume of strata of quadratic differentials, a minimal measured foliation that is not ergodic, and the Thurston norm and its relation to hyperbolic structures.

You will find a brief introduction to Chapters 11-13 below, along with a sampling of illustrations.