Transverse-Legendrian links

TL;DR

This paper extends a Legendrian knot distinguishing technique to transverse knots, demonstrating that the equivalence problem for certain transverse knots is algorithmically solvable, advancing knot theory classification methods.

Contribution

The paper introduces an extension of a Legendrian knot invariant technique to transverse knots and proves the algorithmic solvability of their equivalence problem under specific conditions.

Findings

Extension of Legendrian knot technique to transverse knots

Algorithmic solution for transverse knot equivalence with trivial symmetry group

Future work to remove the triviality condition

Abstract

In recent joint works of the present author with M.Prasolov and V.Shastin a new technique for distinguishing Legendrian knots has been developed. In this paper the technique is extended further to provide a tool for distinguishing transverse knots. It is shown that the equivalence problem for transverse knots with trivial orientation-preserving symmetry group is algorithmically solvable. In a future paper the triviality condition for the orientation-preserving symmetry group will be dropped.