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For a given primitive homology class      ξ  \xi       of      H 2 ( S 2 ×  S 2 ; Z ) {H_2}({S^2} \times {S^2};{\mathbf {Z}})      , we show that there exists only one smoothly embedded      2 2      -sphere in      S 2 ×  S 2 {S^2} \times {S^2}       , up to homeomorphism, which represents      ξ  \xi       and whose complement is simply connected.

Smooth 2-knots in 𝑆²×𝑆² with simply-connected complements are topologically unique