Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142), Volume 142
(Paperback)
Publishing Details
Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142), Volume 142
By (Author) Curtis T. McMullen
Princeton University Press
Princeton University Press
8th October 1996
United States
Classifications
Professional and Scholarly
Non Fiction
Topology
Applied mathematics
516.07
Physical Properties
Paperback
253
Width 197mm, Height 254mm
340g
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.
Reviews
Curtis T. McMullen, Winner of the 1998 Fields Medal, International Congress of Mathematicians "A comprehensive study of a theory which brings into parallel two recent and very deep theorems, involving geometry and dynamics. These are Thurston's theorem on the existence of hyperbolic metrics on three-manifolds which fiber over the circle with pseudo-Anosov monodromy, and Sullivan's theorem on the convergence of the renormalization map for real quadratic mappings... The book is very dense in results and the style is superb."--Mathematical Reviews
Author Bio
Curtis T. McMullen is Professor of Mathematics at the University of California, Berkeley.
