One internal stabilization is enough for resolving self-referential tubes

Abstract

This paper shows that one internal stabilization is enough to resolve all the self-referential tubes on an embedding. As an application, this paper gives a complete isotopy classification for embedded surfaces with a common geometric dual in orientable $S^2$-bundle over a surface, provided that the embedded surfaces have greater genus than the base surface of the bundle.

arXiv comment14 pages, 5 figures. Comments are welcome!