Exoops in two dimensions

An exoop occurs in the gauged linear �-model by varying the Kahler form so that a subspace appears to shrink to a point and then reemerge \outside" the original manifold. This occurs for K3 surfaces where a rational curve is \opped" from inside to outside the K3 surface. We see that whether a rational curve contracts to an orbifold phase or an exoop depends on whether this curve is a line or conic. We study how the D-brane category of the smooth K3 surface is described by the exoop and, in particular, �nd the location of a massless D-brane in the exoop limit. We relate exoops to noncommutative resolutions.