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Research Frontiers in Knot Theory and Link Invariants

Investigates polynomial invariants, quantum invariants, and topological properties of knots and links with applications to molecular biology and quantum computing.

Quantum Invariants and Non-Commutative Topology

Knot Homology Theories Beyond Classical Categorification

Higher-Dimensional Link Invariants and Cobordism

Topological Entanglement in Spatial Graph Embeddings

Invariant Stability Under Deformation and Surgery

Khovanov-Type Invariants in Virtual Knot Spaces

Quantum Groups and Exotic Link Polynomial Structures

Computational Topology of Knot Moduli Spaces

Categorified Quantum Invariants and Representation Theory

Multivalent Invariants in Spatial Isotopy Classification

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