Achievable ranks of intersections of finitely generated free groups

We answer a question due to A. Myasnikov by proving that all expected ranks occur as the ranks of intersections of finitely generated subgroups of free groups.Comment: 4 pages, 4 figure

An Experiment in Model Driven Architecture for e-Enterprise Systems

OMG's Model Driven Architecture demonstrates how a system's specification model can be used within the process of creating supporting software implementations. This article documents the findings of an experiment aimed at determining the extent to which this method of software engineering can be used within the domain of e-Enterprise systems

Slicing, skinning, and grafting

We prove that a Bers slice is never algebraic, meaning that its Zariski closure in the character variety has strictly larger dimension. A corollary is that skinning maps are never constant. The proof uses grafting and the theory of complex projective structures.Comment: 11 pages, 1 figure, to appear in American Journal of Mathematic