Knot Invariant

Knot invariants are mathematical properties that characterize knots, regardless of their spatial embedding. Current research focuses on developing novel methods to compute and relate these invariants, employing techniques like geometric deep learning with graph neural networks and machine learning algorithms to uncover hidden correlations between invariants in different dimensions. These efforts are driven by both theoretical interests in understanding knot topology and practical applications, such as improving defect detection in materials science and automating complex robotic manipulation tasks involving knotted structures. The discovery of new relationships between invariants through machine learning is leading to a deeper understanding of knot theory and its connections to other areas of mathematics and physics.