2003/12/16 by Volodymyr Nekrashevych, Nekrashevych, Volodymyr
Mathematics · #20E08 #28A80 #37B10 #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematics and Applications #math.DS #math.GR #msc:20E08 #msc:28A80 #msc:37B10
paper · pdf · doi:10.48550/arxiv.math/0312306
about 40 pages, 6 figures
arxiv created 2003/12/16 · openalex publication_date 2003/12/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 dynamics of f is related to the group. In particular, the Julia set of f can be reconstructed from \img(f) (from its action on the tree), if f is expanding.