The Resource Renormalization and 3-manifolds which fiber over the circle, by Curtis T. McMullen

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

Label
Renormalization and 3-manifolds which fiber over the circle
Title
Renormalization and 3-manifolds which fiber over the circle
Statement of responsibility
by Curtis T. McMullen
Title variation
Renormalization and three-manifolds which fiber over the circle
Creator
Subject
Language
eng
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 quan
Member of
Cataloging source
CGU
Dewey number
514.3
Index
no index present
LC call number
QA613 .M42 2014
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Annals of Mathematics Studies
Series volume
v. 142
Label
Renormalization and 3-manifolds which fiber over the circle, by Curtis T. McMullen
Publication
Antecedent source
unknown
http://library.link/vocab/branchCode
  • net
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Cover; Title; Copyright; Contents; 1 Introduction; 2 Rigidity of hyperbolic manifolds; 2.1 The Hausdorff topology; 2.2 Manifolds and geometric limits; 2.3 Rigidity; 2.4 Geometric inflexibility; 2.5 Deep points and differentiability; 2.6 Shallow sets; 3 Three-manifolds which fiber over the circle; 3.1 Structures on surfaces and 3-manifolds; 3.2 Quasifuchsian groups; 3.3 The mapping class group; 3.4 Hyperbolic structures on mapping tori; 3.5 Asymptotic geometry; 3.6 Speed of algebraic convergence; 3.7 Example: torus bundles; 4 Quadratic maps and renormalization; 4.1 Topologies on domains
  • 4.2 Polynomials and polynomial-like maps4.3 The inner class; 4.4 Improving polynomial-like maps; 4.5 Fixed points of quadratic maps; 4.6 Renormalization; 4.7 Simple renormalization; 4.8 Infinite renormalization; 5 Towers; 5.1 Definition and basic properties; 5.2 Infinitely renormalizable towers; 5.3 Bounded combinatorics; 5.4 Robustness and inner rigidity; 5.5 Unbranched renormalizations; 6 Rigidity of towers; 6.1 Fine towers; 6.2 Expansion; 6.3 Julia sets fill the plane; 6.4 Proof of rigidity; 6.5 A tower is determined by its inner classes; 7 Fixed points of renormalization
  • 7.1 Framework for the construction of fixed points7.2 Convergence of renormalization; 7.3 Analytic continuation of the fixed point; 7.4 Real quadratic mappings; 8 Asymptotic structure in the Julia set; 8.1 Rigidity and the postcritical Cantor set; 8.2 Deep points of Julia sets; 8.3 Small Julia sets everywhere; 8.4 Generalized towers; 9 Geometric limits in dynamics; 9.1 Holomorphic relations; 9.2 Nonlinearity and rigidity; 9.3 Uniform twisting; 9.4 Quadratic maps and universality; 9.5 Speed of convergence of renormalization; 10 Conclusion; Appendix A. Quasiconformal maps and flows
  • A.1 Conformal structures on vector spacesA. 2 Maps and vector fields; A.3 BMO and Zygmund class; A.4 Compactness and modulus of continuity; A.5 Unique integrability; Appendix B. Visual extension; B.1 Naturality, continuity and quasiconformality; B.2 Representation theory; B.3 The visual distortion; B.4 Extending quasiconformal isotopies; B.5 Almost isometries; B.6 Points of differentiability; B. 7 Example: stretching a geodesic; Bibliography; Index
Control code
ocn921282907
Dimensions
unknown
Extent
1 online resource (264 pages)
File format
unknown
Form of item
online
Isbn
9781400865178
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
http://library.link/vocab/ext/overdrive/overdriveId
22573/ctt767zwm
Quality assurance targets
not applicable
http://library.link/vocab/recordID
.b32058135
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)921282907
  • pebcs1400865174

Library Locations

    • Deakin University Library - Geelong Waurn Ponds CampusBorrow it
      75 Pigdons Road, Waurn Ponds, Victoria, 3216, AU
      -38.195656 144.304955
Processing Feedback ...