Download this article
 Download this article For screen
For printing
Recent Issues
Vol. 338: 1
Vol. 338: 1
Vol. 337: 1  2
Vol. 336: 1
Vol. 335: 1  2
Vol. 334: 1  2
Vol. 333: 1  2
Vol. 332: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
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
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
Authors
Valentina Bais
Scuola Internazionale Superiori di Studi Avanzati (SISSA)
Trieste
Italy
Younes Benyahia
Scuola Internazionale Superiori di Studi Avanzati (SISSA)
Trieste
Italy
The Abdus Salam International Centre for Theoretical Physics (ICTP)
Trieste
Italy
Oliviero Malech
Scuola Internazionale Superiori di Studi Avanzati (SISSA)
Trieste
Italy
Rafael Torres
Scuola Internazionale Superiori di Studi Avanzati (SISSA)
Trieste
Italy

Open Access made possible by participating institutions via Subscribe to Open.