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Organizers |
Circle homeomorphisms and shears
by
Dragomir Saric
The Graduate Center and Queens College of CUNY
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 M[(o)\ddot]b(S1)\Homeo(S1), M[(o)\ddot]b(S1)\QS(S1) and M[(o)\ddot]b(S1)\Symm(S1). To our best knowledge, this gives the only known explicit parametrization of the universal Teichmüller space T(H)=M[(o)\ddot]b(S1)\QS(S1).
Date received: November 25, 2009
Copyright © 2009 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cazp-13.