Legendrian contact homology and nondestabilizability

We provide the first example of a Legendrian knot with nonvanishing contact homology whose Thurston-Bennequin invariant is not maximal.Comment: 12 pages, 2 figure

Higher-dimensional linking integrals

We derive an integral formula for the linking number of two submanifolds of the n-sphere S^n, of the product S^n x R^m, and of other manifolds which appear as "nice" hypersurfaces in Euclidean space. The formulas are geometrically meaningful in that they are invariant under the action of the special orthogonal group on the ambient space.Comment: 10 pages, 3 figure

Lifting Lagrangian immersions in CPn−1\mathbb{C} P^{n-1} to Lagrangian cones in Cn\mathbb{C}^n

In this paper we show how to lift Lagrangian immersions in $\mathbb{C} P^{n-1}$ to produce Lagrangian cones in $\mathbb{C} ^n$, and use this process to produce several families of examples of Lagrangian cones and special Lagrangian cones. Moreover we show how to produce Lagrangian cones, isotopic to the Harvey-Lawson and trivial cones, whose projections to $\mathbb{C} P^{n-1}$ are immersions with few transverse double points.Comment: 28 Pages, 7 figure