We establish various stability results for symplectic surfaces in symplectic 4-manifolds with b+ = 1. These results are then applied to prove the existence of representatives of Lagrangian ADE-configurations as well as to classify negative symplectic spheres in symplectic 4-manifolds with k. This involves the explicit construction of spheres in rational manifolds via a new construction technique called the tilted transport.
Bibliographical noteFunding Information:
The first author was partially supported by the Simons Foundation #246043, the second author by NSF Grant DMS-1207037, and the third author by AMS-Simons travel funds. Moreover, the second and third author were supported by NSF Focused Research Grant DMS-0244663.