Abstract
We prove a structure theorem for locally finite connected graphsX with infinitely many ends admitting a non-compact group of automorphisms which is transitive in its action on the space of ends, Ω X . For such a graphX, there is a uniquely determined biregular treeT (with both valencies finite), a continuous representationφ : Aut(X) → Aut(T) with compact kernel, an equivariant homeomorphism λ : Ω X → Ω T , and an equivariant map τ : Vert(X) → Vert(T) with finite fibers. Boundary-transitive trees are described, and some methods of constructing boundary-transitive graphs are discussed, as well as some examples.
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References
M. J. Dunwoody,Accessibility and groups of cohomological dimension One, Proc. London Math. Soc. (3)38 (1979), 193–215.
M. J. Dunwoody,Cutting up graphs, Combinatorica2 (1) (1982), 15–23.
P. M. Soardi and W. Woess,Amenability, unimodularity and the spectral radius of random walks on infinite graphs, preprint.
J. R. Stallings,Group theory and three dimensional manifolds, Yale Mathematical Monographs, Yale University Press, 1971.
W. Woess,Boundaries of random walks on graphs and groups with infinitely many ends, Isr. J. Math.68(1989), 271–301.
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Nevo, A. A structure theorem for boundary-transitive graphs with infinitely many ends. Israel J. Math. 75, 1–19 (1991). https://doi.org/10.1007/BF02787179
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DOI: https://doi.org/10.1007/BF02787179