$\Lambda$\<Trees and Their Applications
Abstract
To most mathematicians and computer scientists the word ``tree'' conjures up, in addition to the usual image, the image of a connected graph with no circuits. In the last few years various types of trees have been the subject of much investigation, but this activity has not been exposed much to the wider mathematical community. This article attempts to fill this gap and explain various aspects of the recent work on generalized trees. The subject is very appealing for it mixes very naïve geometric considerations with the very sophisticated geometric and algebraic structures. In fact, part of the drama of the subject is guessing what type of techniques will be appropriate for a given investigation: Will it be direct and simple notions related to schematic drawings of trees or will it be notions from the deepest parts of algebraic group theory, ergodic theory, or commutative algebra which must be brought to bear? Part of the beauty of the subject is that the naïve tree considerations have an impact on these more sophisticated topics and that in addition, trees form a bridge between these disparate subjects.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1991
 arXiv:
 arXiv:math/9201265
 Bibcode:
 1992math......1265M
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Dynamical Systems;
 Mathematics  Geometric Topology
 EPrint:
 26 pages. Abstract added in migration.