A recipe for exotic 2-links in closed 4-manifolds whose components are topological unknots

TL;DR

This paper introduces a novel construction of infinite sets of 2-links in closed simply connected 4-manifolds that are topologically unknotted but smoothly inequivalent, revealing new exotic phenomena related to linking.

Contribution

It provides the first known examples of such 2-links with specific 2-link groups, demonstrating exotic Brunnian behavior and emphasizing the role of linking in exotic topology.

Findings

First examples of topologically unknotted, smoothly inequivalent 2-links in 4-manifolds

Examples have surface and free groups as their 2-link groups

Reveals exotic Brunnian behavior related to linking phenomena

Abstract

We describe a construction procedure of infinite sets of $2$-links in closed simply connected 4-manifolds that are topologically isotopic, smoothly inequivalent and componentwise topologically unknotted. These 2-links are the first examples of such kind in the literature. The examples provided have surface and free groups as their 2-link groups. We also point out an exotic Brunnian behaviour of such families, which highlights the important role of linking in creating exotic phenomena.