Cork twisting exotic Stein 4-manifolds

TL;DR

This paper develops methods to construct numerous exotic Stein 4-manifolds and embeddings with identical topological invariants but different smooth structures, expanding understanding of 4-manifold topology.

Contribution

It introduces a technique to generate infinitely many mutually non-diffeomorphic Stein 4-manifolds with the same topological invariants as a given handlebody.

Findings

Constructed many exotic Stein 4-manifolds with identical topological invariants.

Developed a method for creating exotic embeddings of 4-manifolds.

Analyzed contact structures induced on boundaries.

Abstract

From any 4-dimensional oriented handlebody X without 3- and 4-handles and with b_2>0, we construct arbitrary many compact Stein 4-manifolds which are mutually homeomorphic but not diffeomorphic to each other, so that their topological invariants (their fundamental groups, homology groups, boundary homology groups, and intersection forms) coincide with those of X. We also discuss the induced contact structures on their boundaries. Furthermore, for any smooth 4-manifold pair (Z,Y) such that the complement Z-intY is a handlebody without 3- and 4-handles and with b_2>0, we construct arbitrary many exotic embeddings of a compact 4-manifold Y' into Z, such that Y' has the same topological invariants as Y.