Renormalization and 3-Manifolds Which Fiber over the Circle
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A01=Curtis T. McMullen
Analytic continuation
Author_Curtis T. McMullen
Automorphism
Beltrami equation
Bifurcation theory
Boundary (topology)
Cantor set
Category=PBM
Category=PBP
Category=PBW
Combinatorics
Compact space
Complex manifold
Conformal geometry
Conformal map
Conjugacy class
Convex hull
Deformation theory
Degeneracy (mathematics)
Dimension (vector space)
Disk (mathematics)
Eigenvalues and eigenvectors
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Geodesic
Geometry
Hausdorff dimension
Homeomorphism
Homotopy
Hyperbolic 3-manifold
Hyperbolic geometry
Hyperbolic manifold
Hyperbolic space
Infimum and supremum
Injective function
Intersection (set theory)
Isometry
Julia set
Kleinian group
Laplace's equation
Lie algebra
Limit point
Limit set
Mandelbrot set
Manifold
Mobius transformation
Moduli (physics)
Moduli space
Modulus of continuity
N-sphere
Newton's method
Polynomial
Quadratic function
Quasi-isometry
Quasiconformal mapping
Quasisymmetric function
Quotient space (topology)
Radon-Nikodym theorem
Renormalization
Representation theory
Riemann sphere
Riemann surface
Riemannian manifold
Schwarz lemma
Subsequence
Support (mathematics)
Tangent space
Teichmuller space
Theorem
Trace (linear algebra)
Transversal (geometry)
Transversality (mathematics)
Triangle inequality
Unit sphere
Upper and lower bounds
Vector field
Product details
- ISBN 9780691011530
- Weight: 340g
- Dimensions: 197 x 254mm
- Publication Date: 28 Jul 1996
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
Curtis T. McMullen is Professor of Mathematics at the University of California, Berkeley.
