Volume 24, issue 3 (2020)

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

Volume 24
Issue 3, 1075–1614
Issue 2, 533–1073
Issue 1, 1–532

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Isotopies of surfaces in $4$–manifolds via banded unlink diagrams

Mark C Hughes, Seungwon Kim and Maggie Miller

Geometry & Topology 24 (2020) 1519–1569
Abstract

We study surfaces embedded in 4–manifolds. We give a complete set of moves relating banded unlink diagrams of isotopic surfaces in an arbitrary 4–manifold. This extends work of Swenton and Kearton–Kurlin in S4. As an application, we show that bridge trisections of isotopic surfaces in a trisected 4–manifold are related by a sequence of perturbations and deperturbations, affirmatively proving a conjecture of Meier and Zupan. We also exhibit several isotopies of unit surfaces in P2 (ie spheres in the generating homology class), proving that many explicit unit surfaces are isotopic to the standard P1. This strengthens some previously known results about the Gluck twist in S4, related to Kirby problem 4.23.

Keywords
$4$–manifold, knot, surface, diagram
Mathematical Subject Classification
Primary: 57K45
Secondary: 57K40
References
Publication
Received: 20 February 2019
Revised: 29 March 2020
Accepted: 23 May 2020
Published: 30 September 2020
Proposed: András I Stipsicz
Seconded: Mladen Bestvina, Ciprian Manolescu
Authors
Mark C Hughes
Department of Mathematics
Brigham Young University
Provo, UT
United States
https://math.byu.edu/~hughes/
Seungwon Kim
Center for Geometry and Physics
Institute for Basic Science (IBS)
Pohang
South Korea
https://sites.google.com/view/seungwonkim
Maggie Miller
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
https://web.math.princeton.edu/~maggiem