Mathematics

Paul Seidel in his PhD thesis found examples of symplectomorphisms which are smoothly isotopic to the identity, but not Hamiltonian isotopic to the identity. These symplectomorphisms are known as Dehn twists, and they occur every time we have a smooth Lagrangian sphere in a symplectic 4-manifold.Later he proved that Dehn twists are of infinite order in the symplectic mapping class groups of certain symplectic K3 surfaces.In spite of this deep result of Seidel, and other result followed it, we still haveno general way to construct symplectomorphisms for 4-manifolds.For instance, there are 4-manifolds which do not contain Lagrangian spheres, yet they are likely to have the non-trivial symplectic mapping class group.In this talk I will introduce and study a new type of symplectomorphisms for symplectic 4-manifolds.