Gordon-Luecke theorem

Statement
Let $$K_1$$ and $$K_2$$ be two knots (homeomorphic copies of $$S^1$$) in $$S^3$$. Then, any homeomorphism between the knot complements $$S^3 \setminus K_1$$ and $$S^3 \setminus K_2$$ extends to a self-homeomorphism of $$S^3$$. Thus $$K_1$$ and $$K_2$$ sit in the same way (upto possibly a reversal of orientation) inside $$S^3$$.