On elementary moves of singular Legendrian knots

TL;DR

This paper identifies minimal generating sets of singular Reidemeister moves for Legendrian knots and determines which moves are compatible with Legendrian singular knot theory, providing explicit diagrammatic criteria.

Contribution

It provides 96 generating sets for oriented singular Reidemeister moves and explicitly characterizes moves that preserve Legendrian singular knots.

Findings

96 generating sets of singular Reidemeister moves identified

Explicit criteria for Legendrian moves in plane curve and Legendrian knot theory

Surviving moves for Legendrian singular knots determined

Abstract

We have two results. First, we give 96 generating sets oriented singular Reidemeister moves; it is an answer to a question by Bataineh, Khaled, Elhamdadi, and Hajij who give a generating set of oriented singular Reidemeister moves using their computation. Second, in the theory of plane curve and Legendrian knots introduced by V. I. Arnold, we select which moves survive as those of Legendrian singular knots and fronts diagrammatically and explicitly.