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-2 -> $-2$ (for proper typesetting)
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LSpice
LSpice
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Let $S_1$, $S_2$ be homologous embedded 2-spheres in a compact smooth 4-manifold. Under which additional conditions they are they smoothly isotopic? I am interested in the state of the art picture when $S_i$ are spheres with self-intersection -2$-2$ in a K3 surface. However, any related information (for other 4-manifolds, and for extra assumptions on $S_i$, such as Lagrangian or pseudoholomorphic) will be also much appreciated.

I looked around and found many papers about knotted 2-tori and Lagrangian 2-tori in symplectic 4-manifolds, but nothing about knotted 2-spheres.

Let $S_1$, $S_2$ be homologous embedded 2-spheres in a compact smooth 4-manifold. Under which additional conditions they are smoothly isotopic? I am interested in the state of the art picture when $S_i$ are spheres with self-intersection -2 in a K3 surface. However, any related information (for other 4-manifolds, and for extra assumptions on $S_i$, such as Lagrangian or pseudoholomorphic) will be also much appreciated.

I looked around and found many papers about knotted 2-tori and Lagrangian 2-tori in symplectic 4-manifolds, but nothing about knotted 2-spheres.

Let $S_1$, $S_2$ be homologous embedded 2-spheres in a compact smooth 4-manifold. Under which additional conditions are they smoothly isotopic? I am interested in the state of the art picture when $S_i$ are spheres with self-intersection $-2$ in a K3 surface. However, any related information (for other 4-manifolds, and for extra assumptions on $S_i$, such as Lagrangian or pseudoholomorphic) will be also much appreciated.

I looked around and found many papers about knotted 2-tori and Lagrangian 2-tori in symplectic 4-manifolds, but nothing about knotted 2-spheres.

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Misha Verbitsky
Misha Verbitsky
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Isotopy classes of $CP^1$ in 4-manifolds

Let $S_1$, $S_2$ be homologous embedded 2-spheres in a compact smooth 4-manifold. Under which additional conditions they are smoothly isotopic? I am interested in the state of the art picture when $S_i$ are spheres with self-intersection -2 in a K3 surface. However, any related information (for other 4-manifolds, and for extra assumptions on $S_i$, such as Lagrangian or pseudoholomorphic) will be also much appreciated.

I looked around and found many papers about knotted 2-tori and Lagrangian 2-tori in symplectic 4-manifolds, but nothing about knotted 2-spheres.