Trees and Reflection Groups

Humberto Luiz Talpo, Marcelo Firer

Abstract


We define a reflection in a tree as an involutive automorphism whose set of fixed points is a geodesic and prove that, for the case of a homogeneous tree of degree $4k$, the topological closure of the group generated by reflections has index $2$ in the group of automorphisms of the tree.


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