Flexible Surfaces in $\mathbb{C}{P}^2$ and $S^2\times S^2$

Abstract

A surface $\hat{I}\pounds$ in a 4-manifold $M$ is called flexible if any mapping class of the surface arises as the restriction of a diffeomorphism $(M,\hat{I}\pounds )\to (M,\hat{I}\pounds )$. We construct flexible surfaces in $\mathbb{C}{P}^2$ and $S^2\times S^2$ within any prescribed non-characteristic homology class. Within characteristic homology classes there is a spin structure obstructing flexibility and we construct so-called spin-flexible representatives.

19 pages, 9 figures. Comments welcome!