Renormalization and 3-manifolds which fiber over the circle / by Curtis T. McMullen.

Format:

Book

Author/Creator:

McMullen, Curtis T.

Series:

Annals of mathematics studies ; no. 142.

Annals of mathematics studies ; no. 142

Language:

English

Subjects (All):

Three-manifolds (Topology).

Differentiable dynamical systems.

Physical Description:

vii, 253 pages : illustrations ; 24 cm.

Place of Publication:

Princeton, NJ : Princeton University Press, 1996.

Summary:

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.

Notes:

Includes bibliographical references (pages 241-249) and index.

ISBN:

0691011540

0691011532

OCLC:

34690935