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Tree Lattices pp 119-149 | Cite as

Parabolic Actions, Lattices, and Trees

  • Hyman Bass
  • Alexander Lubotzky
Chapter
  • 346 Downloads
Part of the Progress in Mathematics book series (PM, volume 176)

Abstract

Let ε be an end of a tree X. Then VX partitions into “horopheres” X n (nεZ) so that if eε EX is directed toward ε, and δ0eε X n , then δ1eεXn+1. Such edges thus define maps
$$\begin{gathered}\ldots \to \,X_{n - 1} \, \to \,X_{n + 1} \, \to \, \ldots \,,\,\,\,\,with \hfill \\ \underrightarrow {lim\,}X_n \, = \,\left\{ \varepsilon \right\}\,\,\,and\,\,\,\underleftarrow {lim }X_n \, = \,Ends\left( X \right) - \left\{ \varepsilon \right\}. \hfill \\ \end{gathered}$$
(1)

Keywords

Simple Group Tree Lattice Finite Tree Edge Path Linear Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2001

Authors and Affiliations

  • Hyman Bass
    • 1
  • Alexander Lubotzky
    • 2
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsHebrew UniversityJerusalemIsrael

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