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

Valentina Bais, Younes Benyahia, Oliviero Malech and Rafael Torres

Vol. 338 (2025), No. 1, 35–62

DOI: 10.2140/pjm.2025.338.35

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 such examples in the literature. The examples provided have surface and free groups as their 2-link groups, and display subtle exotic phenomena that are related to their linking. In particular, our examples are not parallel copies of exotic embeddings of 2-spheres that were previously known to exist nor their combinations with smoothly unknotted 2-spheres.

Keywords

surfaces, 4-manifolds, exotic smooth structures

Mathematical Subject Classification

Primary: 57K45, 57R55

Secondary: 57R40, 57R52

Milestones

Received: 22 October 2024

Revised: 23 May 2025

Accepted: 28 May 2025

Published: 20 June 2025