Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.
Buy Renormalization and 3-Manifolds Which Fiber Over the Circle book by Curtis T. McMullen from Australia's Online Bookstore, Boomerang Books.
(229mm x 152mm x 14mm)
Princeton University Press
Publisher: Princeton University Press
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