Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Topologically isotopic and smoothly inequivalent $2$–spheres in simply connected $4$–manifolds whose complement has a prescribed fundamental group

Rafael Torres

Algebraic & Geometric Topology 24 (2024) 2351–2365
Abstract

We describe a procedure to construct infinite sets of pairwise smoothly inequivalent 2–spheres in simply connected 4–manifolds, which are topologically isotopic and whose complement has a prescribed fundamental group that satisfies some conditions. This class of groups include cyclic groups and the binary icosahedral group. These are the first known examples of such exotic embeddings of 2–spheres in 4–manifolds. Examples of locally flat embedded 2–spheres in a nonsmoothable 4–manifold whose complements are homotopy equivalent to smoothly embedded ones are also given.

Keywords
knotted surfaces, 4–manifolds
Mathematical Subject Classification
Primary: 57K45, 57R55
Secondary: 57R40, 57R52
References
Publication
Received: 1 December 2022
Revised: 27 March 2023
Accepted: 28 April 2023
Published: 16 July 2024
Authors
Rafael Torres
Scuola Internazionale Superiori di Studi Avanzati (SISSA)
Trieste
Italy

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