Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142), Volume 142

ISBN-10: 1400865174
ISBN-13: 9781400865178
Category: Mathematics
Pages: 253
Language: English
Published: 2014-09-08
Publisher: Princeton University Press
Author: Curtis T. McMullen

Description

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.

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