On diffeomorphisms over surfaces trivially embedded in the 4-sphere

Abstract

A surface in the 4-sphere is trivially embedded, if it bounds a 3dimensional handle body in the 4-sphere. For a surface trivially embedded in the 4-sphere, a diffeomorphism over this surface is extensible if and only if this preserves the Rokhlin quadratic form of this embedded surface. AMS Classification 57N10; 57N05, 20F38 

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