Grid diagram for singular links

Abstract

In this paper, we define the set of singular grid diagrams which provides a unified description for singular links, singular Legendrian links, singular transverse links, and singular braids. We also classify the complete set of all equivalence relations on which induce the bijection onto each singular object. This is an extension of the known result of Ng-Thurston [Grid diagrams, braids, and contact geometry, in Proc. Gökova Geometry-Topology Conf. 2008, Gökova Geometry/Topology Conference (GGT), Gökova, 2009, pp. 120-136] for nonsingular links and braids. © 2018 World Scientific Publishing Company.