knotted 2-spheres in 4-space?

Question

What would be example of "non-trivially" embedded sphere in 4-space and how to visualize?

We could have $S^2 \to \mathbb{R}^4 \subset S^4$ for topologists the 4-space can be "completed" or "compactified" to 4-sphere. Can we get examples of non-trivially embedded 2-knots?

• $\pi_2(S^4 - S^2) = 0$
• $\pi_2(S^4 - S^2) \neq 0$

What do these "shapes" look like? Have I written the invariants correctly? Any good strategies for visualizing such shapes?

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Here is the discussion from Annals in Mathematics from 1959

• Knotted 2-spheres in the 4-sphere this is continuation of the result of Artin in 1930

• Zur Isotopie Zweidimensionaler Flachen in $\mathbb{R}^4$

• Singularities of 2-spheres in 4-space and cobordism of knots