Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142)
Curtis T. McMullen

By the 1998 Fields Medal Winner

Paper | 1996 | $52.50 / £30.95
253 pp. | 6 x 9

Shopping Cart | Reviews | Table of Contents

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.

Review:

"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

Table of Contents

Another Princeton book by Curtis T. McMullen:

• Complex Dynamics and Renormalization (AM-135).

Series:

• Annals of Mathematics Studies
  Phillip A. Griffiths, John N. Mather, and Elias M. Stein, Editors

Subject Area:

• Mathematics

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For customers in the U.S., Canada, Latin America, Asia, and Australia
Paper: $52.50 ISBN13: 978-0-691-01153-0

For customers in Europe, Africa, the Middle East, and India
Paper: £30.95 ISBN13: 978-0-691-01153-0

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