Moscow--Petersburg seminar on low-dimensional mathematics
SPb, PDMI, 22.03.2002, 16:00--17:45, room 311

A.Malyutin
On the action of mapping class groups on one-dimensional manifolds.

Groups acting on topological spaces often occur in mathematics.
Actions of groups on one-dimensional manifolds has recently developed 
into an interesting self-contained theory.
(A simple example showing that this notion is useful:
a group is right orderable if and only if there exists an exact
orientation preserving action of this group on the line.)
For mapping class groups there is an action on the circle defined
by Nielsen a long time ago, and an action on the line defined
by Thurston quite recently. Both actions have a clear geometric 
meaning.

It turns out that both actions are particular cases of a unified
construction that also yields new actions of mapping class groups
on one-dimensional manifolds. The talk is dedicated to this construction
and its applications.