Exponential growth of some iterated monodromy groups
نویسندگان
چکیده
منابع مشابه
Iterated Monodromy Groups
We associate a group IMG(f) to every covering f of a topological space M by its open subset. It is the quotient of the fundamental group π1(M) by the intersection of the kernels of its monodromy action for the iterates fn. Every iterated monodromy group comes together with a naturally defined action on a rooted tree. We present an effective method to compute this action and show how the dynamic...
متن کاملIterated Monodromy Groups of Quadratic Polynomials, I
We describe the iterated monodromy groups associated with post-critically finite quadratic polynomials, and explicit their connection to the ‘kneading sequence’ of the polynomial. We then give recursive presentations by generators and relations for these groups, and study some of their properties, like torsion and ‘branchness’.
متن کاملExponential Iterated Integrals and Solvable Completions of Fundamental Groups
We develop a class of integrals on a manifold called exponential iterated integrals, an extension of K. T. Chen’s iterated integrals. It is shown that these integrals can be used to compute the matrix entries of certain solvable representations of the fundamental group of the manifold. In particular we find that exponential iterated integrals separate the elements of groups of fibered knots.
متن کاملUniform Growth in Groups of Exponential Growth
This is an exposition of examples and classes of finitely-generated groups which have uniform exponential growth. The main examples are non-Abelian free groups, semi-direct products of free Abelian groups with automorphisms having an eigenvalue of modulus distinct from 1, and Golod–Shafarevich infinite finitely-generated p-groups. The classes include groups which virtually have non-Abelian free...
متن کاملThe spectral problem, substitutions and iterated monodromy
We provide a self-similar measure for the self-similar group G acting faithfully on the binary rooted tree, defined as the iterated monodromy group of the quadratic polynomial z + i. We also provide an Lpresentation for G and calculations related to the spectrum of the Markov operator on the Schreier graph of the action of G on the orbit of a point on the boundary of the binary rooted tree.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2018
ISSN: 0024-6115
DOI: 10.1112/plms.12118