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We construct invariants of colored links using equivariant bordism groups ofConner and Floyd. We employ this bordism invariant to find the first examplesof topological vortex knots, the knot structure of which is protected fromdecaying via topologically allowed local surgeries, i.e., by reconnections andstrand crossings permitted by the topology of the vortex-supporting medium.Moreover, we show that, up to the aforementioned local surgeries, eachtricolored link either decays into unlinked simple loops, or can be transformedinto either a left-handed or a right-handed tricolored trefoil knot.

Bordism invariants of colored links and topologically protected tricolorings