Thursday, January 24, 2013

1301.5446 (A. V. Nazarenko)

Two-parametric hyperbolic octagons and reduced Teichmueller space in
genus two

A. V. Nazarenko
It is explored a model of compact Riemann surfaces in genus two, represented geometrically by two-parametric hyperbolic octagons with an order four automorphism. We compute the generators of associated isometry group and give a real-analytic description of corresponding Teichm\"uller space, parametrized by the Fenchel-Nielsen variables, in terms of geometric data. We state the structure of parameter space by computing the Weil-Petersson symplectic two-form and analyzing the isoperimetric orbits. The results of the paper may be interesting due to their applications to the quantum geometry, chaotic systems and low-dimensional gravity.
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