Exotic codimension-1 submanifolds in 4-manifolds and stabilizations

Abstract

In a small simply-connected closed 4-manifold, we construct infinitely many pairs of exotic codimension-$1$ submanifolds with diffeomorphic complements that remain exotic after any number of stabilizations by $S^2\times S^2$. We also give new constructions of exotic embeddings of 3-spheres in 4-manifolds with diffeomorphic complements.

10 pages, 1 figure, An error in one of main results (Theorem 1.4, corresponding to Theorem 1.3 of v1) was corrected by restricting a class of 3-manifolds in the statement. The authors are grateful to Inanc Baykur for pointing out the mistake in v1. We changed the introduction accordingly and added a few new questions and remarks