Grid Homology in the Theory of Legendrian and Transverse Knots

Abstract

This paper is a presentation of the application of grid homology, a recently developed area in the study of knot theory, to the theory of Legendrian and transverse knots. The first chapter covers the classical theory of Legendrian and transverse knots. The second chapter introduces grid structures and grid homology, and the third chapter demonstrates the application of grid homology to Legendrian and transverse knot theory, in particular showing examples found through grid homology of non-isotopic Legendrian and transverse knots which cannot be distinguished through their classical invariants.