Circle homeomorphisms and shears

Geometry & Topology
Event time: 
Tuesday, April 13, 2010 - 9:30am to Monday, April 12, 2010 - 8:00pm
215 LOM
Dragomir Saric
Speaker affiliation: 
Event description: 

The space of homeomorphisms Homeo(S1) of the unit circle S1 is a classical topological group which acts on S1. Homeo(S1) contains many important subgroups such as the infinite dimensional Lie group Diffeo(S1) of diffeomorphisms of S1, the group QS(S1) of quasisymmetric maps of S1, the characteristic topological group Symm(S1) of symmetric maps of S1, and many more. We use the shear coordinates on the Farey tesselation to parametrize the coadjoint orbit spaces Möb(S1) \ Homeo(S1), Möb(S1) \ QS(S1) and Möb(S1) \ Symm(S1). To our best knowledge, this gives the only known explicit parametrization of the universal Teichmüller space T(H)= Möb(S1) \ QS(S1).