Knottings of orientable surfaces in 1-connected 4-manifolds.

摘要

Recent developments in the study of the relationship between the topology and geometry of 4-manifolds have resulted in the discovery of many so called exotic structures. These are non-compatible smooth structures on the same topological manifold.;If N is a closed submanifold of a closed manifold M of dimension not equal to 4, and U is its tubular neighborhood, then there are only finitely many diffeomorphism types relative boundary to M;S. M. Finashin, M. Kreck and O. Y. Viro in their paper (Non-Diffeomorphic but Homeomorphic knottings of Surfaces in the 4-Sphere, LNM, v. 1346, Springer, 1988, pp. 157-198) found a counter-example to the above statement where N is ;This paper is an attempt to find examples where the surface N is orientable. In it, embeddings of orientable surfaces in simply-connected 4-manifolds which are promising candidates to a counter-example of the above theorem are exhibited. This involves the construction of antiholomorphic involutions on Kodaira's homotopy K3 surfaces K