Corks, Plugs and exotic structures

TL;DR

This paper introduces new objects called plugs that, like corks, detect exotic smooth structures in 4-manifolds, and explores their relationships and constructions, including knotted variants.

Contribution

It presents the concept of plugs as new tools for detecting exotic structures, extending the theory of corks, and demonstrates their relation to rational blow-downs and knotted examples.

Findings

Plugs can detect exotic smooth structures in 4-manifolds.

Construction of knotted corks and plugs.

Relation between corks, plugs, and rational blow-downs.

Abstract

We discuss corks, and introduce new objects which we call plugs. Though plugs are fundamentally different objects, they also detect exotic smooth structures in 4-manifolds like corks. We discuss relation between corks, plugs and rational blow-downs. We show how to detect corks and plugs inside of some exotic manifolds. Furthermore, we construct knotted corks and plugs.