Renormalization and 3-manifolds Which Fiber Over the Circle (am-142) (ebook)

Argumento de Renormalization and 3-manifolds Which Fiber Over the Circle (am-142) (ebook)

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.01 Introduction 1 2 Rigidity of hyperbolic manifolds 11 3 Three-manifolds which fiber over the circle 41 4 Quadratic maps and renormalization 75 5 Towers 95 6 Rigidity of towers 105 7 Fixed points of renormalization 119 8 Asymptotic structure in the Julia set 135 9 Geometric limits in dynamics 151 10 Conclusion 175 Appendix A. Quasiconformal maps and flows 183 Appendix B. Visual extension 205 Bibliography 241 Index 251