Geodesic
The symmetries of McCullough--Miller space
Algebra and discrete mathematics, Tome 14 (2012) no. 2, pp. 239-266

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We prove that if $W$ is the free product of at least four groups of order $2$, then the automorphism group of the McCullough-Miller space corresponding to $W$ is isomorphic to group of outer automorphisms of $W$. We also prove that, for each integer $n \geq 3$, the automorphism group of the hypertree complex of rank $n$ is isomorphic to the symmetric group of rank $n$.
Keywords: Autmorphisms of groups; group actions on simplicial complexes; Coxeter groups; McCullough-Miller space; hypertrees. 
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     author = {Adam Piggott},
     title = {The symmetries of {McCullough--Miller} space},
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     number = {2},
     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a8/}
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Adam Piggott. The symmetries of McCullough--Miller space. Algebra and discrete mathematics, Tome 14 (2012) no. 2, pp. 239-266. http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a8/