立体连通性轨迹I的地理学：交织手术
Geography of the cubic connectedness locus I: Intertwining surgery
摘要：
我们展示了三次多项式的二维复参数空间中的Mandelbrot集的乘积。这些产物由J. Milnor在计算机实验中观察到，激发了Lavaurs对立方连通性轨迹的非局部连通性的证明。在这样的乘积中的三次多项式可以被重整化以产生一对二次映射。逆构造是两个二次曲线上的{ \it交织运算}。交织的想法首先出现在收集的问题编辑的比勒费尔德。使用拟共形手术技术的Branner和Douady，我们表明，任何两个二次曲线可以交织在一起，以获得一个三次多项式。在我们的两个参数设置的连续性的证明需要进一步的考虑，涉及射线组合和拉回参数。
英文摘要：
We exhibit products of Mandelbrot sets in the two-dimensional complex parameter space of cubic polynomials. These products were observed by J. Milnor in computer experiments which inspired Lavaurs' proof of non local-connectivity for the cubic connectedness locus. Cubic polynomials in such a product may be renormalized to produce a pair of quadratic maps. The inverse construction is an {\it intertwining surgery} on two quadratics. The idea of intertwining first appeared in a collection of problems edited by Bielefeld. Using quasiconformal surgery techniques of Branner and Douady, we show that any two quadratics may be intertwined to obtain a cubic polynomial. The proof of continuity in our two-parameter setting requires further considerations involving ray combinatorics and a pullback argument.
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