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Geometriae Dedicata

, Volume 92, Issue 1, pp 195–233 | Cite as

Maximally Symmetric Trees

  • Lee Mosher
  • Michah Sageev
  • Kevin Whyte
Article

Abstract

We characterize the “best” model geometries for the class of virtually free groups, and we show that there is a countable infinity of distinct “best” model geometries in an appropriate sense – these are the maximally symmetric trees. The first theorem gives several equivalent conditions on a bounded valence, cocompact tree T without valence 1 vertices saying that T is maximally symmetric. The second theorem gives general constructions for maximally symmetric trees, showing for instance that every virtually free group has a maximally symmetric tree for a model geometry.

virtually free groups maximally symmetric trees 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Lee Mosher
    • 1
  • Michah Sageev
    • 2
  • Kevin Whyte
    • 3
  1. 1.Department of MathematicsRutgers UniversityNewarkU.S.A
  2. 2.Department of MathematicsTechnion, Israel University of TechnologyHaifaIsrael
  3. 3.Department of MathematicsUniversity of ChicagoChicagoU.S.A.

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