Cubic Hecke algebras and invariants of transversal links

Abstract

Let α be a differential 1�form which defines the standard (tight) contact structure in 3 , e.g., α = xdy – ydx + dz. A link L in 3 is called transversal if α| L does not vanish on L. Transversal links are considered up to isotopies such that the link remains transversal at every moment. Transversal links and their invariants are being actively studied, see, e.g., [2, 6, 7, 11] and numerous references therein. In the present paper, we propose a purely algebraic approach to construct invariants of transversal links (similar to Jones’ approach [5] to construct invariants of usual links). The only geometry used is the transversal analogue of Alexander’s and Markov’s theorems proved in [1] and [10] respectively.