Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps

* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.

Numerical Approximation of a Fractional-In-Space Diffusion Equation, I

2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary)

On Compositions in Equiaffine Space

In an equiaffine space q N E using the connection define with projective tensors na and ma the connections 1 , 2 and 3 . For the spaces N N 1A ,2A and N 3A , with coefficient of connection 1 , 2 and 3 respectively, we proved that the affinor of composition and the projective affinors have equal covariant derivatives. It follows that the connection 3 is equaffine as well, and the connections and 3 are projective to each other. In the case where q N E and N 3A have equal Ricci tensors, we find the fundamental nvector . In [4] compositions with structural affinor a are studied. Space containing compositions with symmetric connection and Weyl connection are studied in [6] and [7] respectively.

On Compositions in Equiaffine Space

In an equiaffine space q N E using the connection define with projective tensors na and ma the connections 1 , 2 and 3 . For the spaces N N 1A ,2A and N 3A , with coefficient of connection 1 , 2 and 3 respectively, we proved that the affinor of composition and the projective affinors have equal covariant derivatives. It follows that the connection 3 is equaffine as well, and the connections and 3 are projective to each other. In the case where q N E and N 3A have equal Ricci tensors, we find the fundamental nvector . In [4] compositions with structural affinor a are studied. Space containing compositions with symmetric connection and Weyl connection are studied in [6] and [7] respectively.

Multipliers on Spaces of Functions on a Locally Compact Abelian Group with Values in a Hilbert Space

2000 Mathematics Subject Classification: Primary 43A22, 43A25.

Linear Colligations and Dynamic System Corresponding to Operators in the Banach Space

2000 Mathematics Subject Classification: Primary 47A48, 93B28, 47A65; Secondary 34C94.

Predegree Polynomials of Plane Configurations in Projective Space

2000 Mathematics Subject Classification: 14N10, 14C17.