Classical knot theory, topology and geometry of 3-manifolds, algebraic topology based on knots, secondary: Graph theory, hyperbolic geometry, 4-manifolds, statistical mechanics, representations of Lie algebras and Hopf algebras (quantum groups), Hecke algebras, character varieties, symplectic structures, Hochschild homology, cyclic homology, distributive homology, entropic magmas,, Yang-Baxter homology, (co)cycle invariants of links

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