A polynomial invariant for links in lens spaces

We prove the existence of a polynomial invariant that satisfies the HOMFLY skein relation for links in a lens space. In the process we also develop a skein theory of toroidal grid diagrams in a lens space.Comment: 31 pages, 23 figures; final revision for publicatio

Bennequin type inequalities in lens spaces

We give criteria for an invariant of lens space links to bound the maximal self-linking number in certain tight contact lens spaces. As a corollary we extend the Franks-Williams-Morton inequality to the setting of lens spaces.Comment: 21 pages, 13 figures; International Mathematics Research Notices 201

Knot contact homology and representations of knot groups

We study certain linear representations of the knot group that induce augmentations of knot contact homology. This perspective on augmentations enhances our understanding of the relationship between the augmentation polynomial and the A-polynomial of the knot. For example, we show that for 2-bridge knots the polynomials agree and that this is never the case for (non-2-bridge) torus knots, nor for a family of 3-bridge pretzel knots. In addition, we obtain a lower bound on the meridional rank of the knot. As a consequence, our results give another proof that torus knots and a family of pretzel knots have meridional rank equal to their bridge number.Comment: revision, published in J. Topolog

Productivity convergence and economic growth: A frontier production function approach

The empirical growth literature has focused on capital accumulation but largely ignored productivity growth. To address this imbalance, we propose a methodology for analyzing productivity convergence based on frontier production functions. We examine whether departures from the frontier are cointegrated, determine the extent and speed of catch-up, and assess the importance of efficiency changes for economic growth. Using a sample of 26 OECD countries from 1965-90, we find convergence and catch-up is fairly strong among EU countries but not among the G-7. Overall, the ability to absorb new technology is an important source of economic growth. --cointegration,convergence,growth,productivity,unit root