XXII WORKSHOP ON GEOMETRIC METHODS IN PHYSICS
29 JUNE - 5 JULY 2003, BIAŁOWIEŻA, POLAND
Lieva Beklaran -
Structure of the groups of homeomorphisms of the real line and circle
The groups of homeomorphisms of the real line and circle are universal
object of the groups theory. On the other hand, at study of many problems
of geometry, the functions theory of the complex variable, the dynamic
systems which are reduced to systems of small dimension, the basic
obstacle is been the structure of the group of homeomorphisms of real
line (circle), which is generated canonical image by initial problem.
Therefore, the study of structure of such groups is actual. The report is
devoted to investigation of the major characteristics of the group of
homeomorphisms of the real line (circle). Topological, metric, algebraic
and combinatory characteristics are concerned to them. The basic part of
my report will be devoted to correlations between characteristics having
a various nature.