Grid diagram for singular links
Byung Hee An, Hwa Jeong Lee
TL;DR
This paper introduces singular grid diagrams as a unified framework for various singular link types and classifies their equivalence relations, extending previous results for non-singular links.
Contribution
It defines singular grid diagrams and classifies all equivalence relations, extending Ng-Thurston's work to singular links and braids.
Findings
Unified description for singular links and related objects
Complete classification of equivalence relations on singular grid diagrams
Extension of Ng-Thurston's results to singular cases
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 for non-singular links and braids.
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