Let $K_1$ and $K_2$ be two oriented links in $S^3$ an let $\phi : S^3 \to S^3$ be a diffeomorphism. Is $lk(K_1,K_2) = lk(\phi(K_1), \phi(K_2))$?
2026-03-29 10:37:10.1774780630
Is linking number invariant under automorphisms of $S^3$?
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Yes. And you can prove it using homology.