Self-Similar Groups

By Volodymyr V. Nekrashevych. 2005

655 citations recorded by the source corpus.

Basic definitions and examples Algebraic theory Limit spaces Orbispaces Iterated monodromy groups Examples and applications Bibliography Index.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0011de3a8cc00f1797de240f09daf034bfe47a22

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Citations in the corpus

Groups St Andrews 2005: Self-similarity and branching in group theory (2007, background): “Of particular importance, is the relationship of self-similar groups to Julia sets and fractals from holomorphic dynamics via iterated monodromy groups, introduced by Nekrashevych [5].”
Schreier graphs of the Basilica group (2009, background): “) In particular, the inflation recursive process of constructing finite Schreier graphs introduced in [12] (and used in [5] to study growth of infinite Schreier graphs) might also give a possible general approach to classification of infinite Schreier graphs of contracting groups of automorphisms of”
Homogeneous trees of second order Sturm-Liouville equations: A general theory and program (2008, background): “One of the simple but crucial ideas in this topic in particular, and in quantum (as well as combinatorial) graph research in general, is usage of the so called Dirichlet-to-Neumann map that enables one to eliminate the scatterer sitting at the vertex and replace it with an energy dependent vertex co”
Graph inverse semigroups: their characterization and completion (2011, background): “This paper shows that the self-similar groups of [39] are in bijective correspondence with what we would now call 0-bisimple Perrot monoids.”
Thurston equivalence of topological polynomials (2005, background): “In the terminology of [8], this means that the GC -bimodule F is irreducible.”
On a series of finite automata defining free transformation groups (2006, methodology): “10 ([Nek]) The dual automaton of the Bellaterra automaton defines a transformation group that acts transitively on each level of the rooted subtree of {a, b, c} formed by no-double-letter words.”
Self-similar graphs, a unified treatment of Katsura and Nekrashevych C*-algebras (2014, background): “The condition relies on two concepts associated to self-similar groups: self-replication and contractiveness (see [26] or [25] for the definitions).”
Arboreal Galois representations (2007, background): “It is well-known (Nekrashevych, 2005, Proposition 1.4.2) that Aut(Tn) is isomorphic to the n-fold iterated wreath product of the symmetric group Sd, which we denote by Wn (the value of d will always be clear from context; usually it will be 2).”