Thurston Equivalence of Topological Polynomials
نویسندگان
چکیده
We answer Hubbard’s question on determining the Thurston equivalence class of “twisted rabbits”, i.e. composita of the “rabbit” polynomial with nth powers of the Dehn twists about its ears. The answer is expressed in terms of the 4-adic expansion of n. We also answer the equivalent question for the other two families of degree-2 topological polynomials with three post-critical points. In the process, we rephrase the questions in group-theoretical language, in terms of wreath recursions.
منابع مشابه
Thurston Equivalence to a Rational Map Is Decidable
We demonstrate that the question whether or not a given topological ramified covering map of the 2-sphere is Thurston equivalent to a rational map is algorithmically decidable.
متن کاملOn the topological equivalence of some generalized metric spaces
The aim of this paper is to establish the equivalence between the concepts of an $S$-metric space and a cone $S$-metric space using some topological approaches. We introduce a new notion of a $TVS$-cone $S$-metric space using some facts about topological vector spaces. We see that the known results on cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained from...
متن کاملTopological Equivalence of Complex Polynomials
The following numerical control over the topological equivalence is proved: two complex polynomials in n 6= 3 variables and with isolated singularities are topologically equivalent if one deforms into the other by a continuous family of polynomial functions fs : C → C with isolated singularities such that the degree, the number of vanishing cycles and the number of atypical values are constant ...
متن کاملTopological structure on generalized approximation space related to n-arry relation
Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...
متن کاملNon Reality and Non Connectivity of Complex Polynomials
Using the same method we provide negative answers to the following questions: Is it possible to find real equations for complex polynomials in two variables up to topological equivalence (Lee Rudolph)? Can two topologically equivalent polynomials be connected by a continuous family of topologically equivalent polynomials?
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004