Horocyclic products of trees

@inproceedings{Bartholdi2006HorocyclicPO,
  title={Horocyclic products of trees},
  author={Laurent Bartholdi and Markus Neuhauser and Wolfgang Woess},
  year={2006}
}
Let T1, . . . , Td be homogeneous trees with degrees q1 + 1, . . . , qd + 1 ≥ 3, respectively. For each tree, let h : Tj → Z be the Busemann function with respect to a fixed boundary point (end). Its level sets are the horocycles. The horocyclic product of T1, . . . , Td is the graph DL(q1, . . . , qd) consisting of all d-tuples x1 · · ·xd ∈ T1×· · ·×Td with h(x1) + · · ·+ h(xd) = 0, equipped with a natural neighbourhood relation. In the present paper, we explore the geometric, algebraic… CONTINUE READING