# at.algebraic topology – Embedding with vanishing images of homotopy groups

Let $$f$$ be a locally flat embedding from $$S^2 times mathbb R^2$$ to $$S^2 times mathbb R^2$$ such that $$f_*(pi_k(S^2 times mathbb R^2))=0$$ for any $$k ge 2$$.

Can we find a domain $$U$$ that contains the image of $$f$$ such that $$U$$ is homeomorphic to $$mathbb R^4$$?