Some properties of grid homology for MOY graphs
Hajime Kubota
TL;DR
This paper explores properties of grid homology for MOY graphs, including skein relations and effects of edge contractions and unions, extending the understanding of graph invariants in knot theory.
Contribution
It introduces new properties of grid homology for MOY graphs, expanding on previous work by Harvey and O'Donnol with specific relations and transformations.
Findings
Established the oriented skein relation for MOY graphs
Analyzed the effect of contracting edges on grid homology
Studied the impact of uniting parallel edges with same orientation
Abstract
Grid homology for MOY graphs is immediately defined from grid homology for transverse spatial graphs developed by Harvey and O'Donnol in 2017. We studied some properties of grid homology for MOY graphs such as the oriented skein relation, the effect of contracting an edge, and the effect of uniting parallel edges with the same orientation.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Computational Geometry and Mesh Generation · Homotopy and Cohomology in Algebraic Topology