Teichmüller space for hyperkähler and symplectic structures

Algebraic Structures on Hyperkähler Manifolds Algebraic Structures on Hyperkähler Manifolds

Let M be a compact hyperkähler manifold. The hy-perkähler structure equips M with a set R of complex structures parametrized by CP 1 , called the set of induced complex structures. It was known previously that induced complex structures are non-algebraic, except may be a countable set. We prove that a countable set of induced complex structures is algebraic, and this set is dense in R. A more g...

Quantum Teichmüller Space

We describe explicitly a noncommutative deformation of the *-algebra of functions on the Teichmüller space of Riemann surfaces with holes equivariant w.r.t. the mapping class group action.

Hyperkähler embeddings and holomorphic symplectic geometry I. Mikhail Verbitsky,

Hyperkähler embeddings and holomorphic symplectic geometry I. 0. Introduction. In this paper we are studying complex analytic subvarieties of a given Kähler manifold which is endowed with a holomorphic symplectic structure. By Calabi-Yau theorem, the holomorphically symplectic Kähler mani-folds can be supplied with a Ricci-flat Riemannian metric. This implies that such manifolds are hyperkähler...

Dynamics over Teichmüller Space

Fuzzy Subgroups and the Teichmüller Space

There exists a generalization of the Teichmüller space of a covering group. In this paper we combine this generalized Teichmüller space T (G) and any fuzzy subgroup A : G−→ F where G is a subgroup of the group consisting of such orientation preserving and orientation reversing Möbius transformations which act in the upper half-plane of the extended complex plane. A partially ordered set F = (F ...