Geometry, Topology and Dynamics Seminar
Alvaro Martinez-Perez
Quasi-isometries between bushy trees
Abstract: Quasi-isometries between R-trees induce power quasi-symmetric (or PQ-symmetric) homeomorphisms
between their ultrametric end spaces. Also, PQ-symmetric homeomorphisms between bounded, complete, ultrametric spaces (i.e., those
ultrametric spaces arising up to similarity as the end spaces of R-trees) can be extended to quasi-isometries between the trees.
A bounded distortion property is found that characterizes power quasi-symmetric homeomorphisms
between such ultrametric spaces that are also pseudo-doubling (in particular, for those arising up to similarity as the end spaces of bushy R-trees).
This can be used to define a metric between rooted geodesically complete simplicial trees with minimal vertex degree 3 in the same quasi-isometry class. We also show how this map for larger categories of trees, although it is not a metric, being 0 characterizes the ramification of the tree.
Part of this is a joint work with B. Hughes (Vanderbilt U.) and Manuel A. Moron (UCM).
Monday March 29, 2010 at 3:00 PM in SEO 612