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Colloidal particles dispersed in liquid crystals induce nematic fields and topological defects that are dictated by the topology of the colloidal particles. However, little is known about such interplay of topologies. It is now shown that knot-shaped microparticles in liquid crystals induce defect lines that get entangled with the colloidal knots, and that such mutually tangled configurations satisfy topological constraints and follow predictions from knot theory.