Circle homeomorphisms and shears

Dragomir Saric

Knots in Washington XXIX; 30 years of quandles, 10 years of Khovanov homology
December 4-6, 2009
George Washington University
Washington, DC, USA

Organizers
Jozef H. Przytycki (GWU), Yongwu Rong (GWU, NSF), Radmila Sazdanovic (GWU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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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