Search

It was suggested in [5] that for arithmetic groups Invariable Generation is equivalent to the Congruence Subgroup Property. In this paper, we dismiss this conjecture by proving that certain arithmetic groups which possess the later property do not possess the first one. [ABSTRACT FROM AUTHOR]

We establish the leafwise intersection property for closed, coisotropic submanifolds in an exact symplectic manifold satisfying natural additional assumptions. [ABSTRACT FROM PUBLISHER]

In the moduli space of quadratic differentials over complex structures on a surface, we construct a set of full Hausdorff dimension of points with bounded Teichmüller geodesic trajectories. The main tool is quantitative nondivergence of Teichmüller horocycles, due to Minsky and Weiss. This has an application to billiards in rational polygons. [ABSTRACT FROM AUTHOR]

Motivated by some results in classical differential geometry, we give a constructive procedure for building up a connection over a (twisted) tensor product of two algebras, starting from connections defined on the factors. The curvature for the product connection is explicitly calculated, and shown to be independent of the choice of the twisting map and the module twisting map used to define the product connection. As a consequence, we obtain that a product of two flat connections is again a flat connection. We show that our constructions also behave well with respect to bimodule structures, namely being the product of two bimodule connections again a bimodule connection. As an application of our theory, all the product connections on the quantum plane are computed. [ABSTRACT FROM PUBLISHER]

We give a lower bound on the size of the product set of two arbitrary subsets of the set of Farey fractions of a given order and apply it to study the distribution of elements of multiplicative groups in residue rings. For example, we prove a conjecture of J. Holden and P. Moree on the behavior of the number of solutions to the congruence gh ≡ h (mod p), 1 ≤ g,h ≤ p - 1, on average over primes p. This congruence appears in studying fixed points of the discrete logarithm. [ABSTRACT FROM PUBLISHER]

Let be a closed symplectic manifold and the group of Hamiltonian diffeomorphisms of . Then the Seidel homomorphism is a map from the fundamental group of to the quantum homology ring . Using this homomorphism, we give a sufficient condition for when a nontrivial loop in determines a nontrivial loop in , where is a closed symplectic manifold such that . [ABSTRACT FROM PUBLISHER]