Surfaces in 4-manifolds and their mapping class groups
There are deformations of embedded surfaces in 4-manifolds which induce isotopically non-trivial diffeomorphisms on surfaces. These deformations define extensions of isotopically non-trivial diffeomorphisms on surfaces. It is known that any orientation preserving diffeomorphism of a surface embedded in the complex projective plane is extendable. In the present paper, the authors investigate embedded surfaces in some other smooth 4-manifolds, for which the same kind of phenomena happen. A surface in a smooth 4-manifold is called flexible if, for any diffeomorphism \(\phi\) on the surface, there is a diffeomorphism on the 4-manifold whose restriction to the surface is \(\phi\) and which is isotopic to the identity. The authors investigate a sufficient condition for a smooth 4-manifold \(M\) to include flexible knotted surfaces. They also introduce a local operation in simply connected 4-manifolds for obtaining a flexible knotted surface from any knotted surface.
scientific article; zbMATH DE number 5544217