Published online by Cambridge University Press: 05 February 2014
The firm intention of writing this book was born in the fall of 2003 during the Ecole Thématique du CNRS Chirurgie holomorphe. This workshop was part of a trimester organized by Adrien Douady at the Institut Henri Poincaré in Paris. Douady was one of the fathers of the theory of holomorphic dynamics and of many of the surgery constructions that the workshop addressed. He used surgery as a tool in a number of ways, but especially to obtain a better understanding of different structures in parameter space. As he said: ‘plough in dynamical spaces and harvest in parameter space’.
Douady's creative and geometric point of view inspired many to explore holomorphic dynamics. Furthermore, he encouraged generous collaboration and believed strongly in the value of sharing ideas. He gathered a large mathematical family around him, and the success of the workshop is a tribute to his influence.
Many of those who had originally developed holomorphic surgery presented lectures. It became clear that the content of these wonderful sessions ought to be the core of a book about surgery. We ourselves felt strongly that the book should be more than a collection of papers, though: our goal became to enlist the help of the speakers in creating a comprehensive study of quasiconformal surgery.
We are delighted that our wishes have come true in the form of this book, which puts together the foundations of surgery and many of its applications, with, as we had hoped, contributions by a number of the workshop participants who themselves had played such an important part in developing the field.
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