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

Rolf-Peter, Holzapfel (1997)

Serdica Mathematical Journal

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....

Symplectic torus bundles and group extensions.

Kahn, Peter J. (2005)

The New York Journal of Mathematics [electronic only]

Syntactic congruences and syntactic algebras

Johannes Arz (1983)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Syntaktische Monoide und Hypercodes.

E. Valkema (1976/1977)

Semigroup forum

System of equations in commuting variables for free products of Abelian groups.

Esyp, E.S. (2006)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

Systèmes sous-elliptiques

J. Nourrigat (1986/1987)

Séminaire Équations aux dérivées partielles (Polytechnique)

Systems of equations over locally p-indicable groups.

Sava Krstic (1985)

Inventiones mathematicae

Systems of homogeneous equations

Wolfgang M. SCHMIDT (1981/1982)

Seminaire de Théorie des Nombres de Bordeaux

Systoles of arithmetic surfaces and the Markoff spectrum.

Paul Schmutz (1996)

Mathematische Annalen

Systolic groups acting on complexes with no flats are word-hyperbolic

Piotr Przytycki (2007)

Fundamenta Mathematicae

We prove that if a group acts properly and cocompactly on a systolic complex, in whose 1-skeleton there is no isometrically embedded copy of the 1-skeleton of an equilaterally triangulated Euclidean plane, then the group is word-hyperbolic. This was conjectured by D. T. Wise.

Systolic invariants of groups and $2$ -complexes via Grushko decomposition

Yuli B. Rudyak, Stéphane Sabourau (2008)

Annales de l’institut Fourier

We prove a finiteness result for the systolic area of groups. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of $2$ -complexes whose systolic area is uniformly bounded. We also show that the number of freely indecomposable such groups grows at least exponentially with the bound on the systolic area. Furthermore, we prove a uniform systolic inequality for all $2$ -complexes with unfree fundamental group that improves the previously known bounds in this dimension....