Exotic codimension-1 submanifolds in 4-manifolds and stabilizations

TL;DR

This paper constructs infinitely many exotic codimension-1 submanifold pairs in 4-manifolds with diffeomorphic complements that stay exotic after stabilization, and introduces new exotic 3-sphere embeddings with diffeomorphic complements.

Contribution

It provides new examples of exotic submanifolds and embeddings in 4-manifolds with stable complements, advancing understanding of exotic phenomena in 4-dimensional topology.

Findings

Existence of infinitely many exotic codimension-1 submanifold pairs with stable exotic complements

New constructions of exotic 3-sphere embeddings in 4-manifolds

Exotic features persist under stabilization by S^2 × S^2

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.