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Isotopies of surfaces in
$4$–manifolds via banded unlink diagrams
Mark C Hughes, Seungwon Kim and Maggie Miller |
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Geometry & Topology 24 (2020) 1519–1569
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Abstract |
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We study surfaces embedded in –manifolds. We give a complete set of moves relating banded unlink diagrams of isotopic surfaces in an arbitrary –manifold. This extends work of Swenton and Kearton–Kurlin in . As an application, we show that bridge trisections of isotopic surfaces in a trisected –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 (ie spheres in the generating homology class), proving that many explicit unit surfaces are isotopic to the standard . This strengthens some previously known results about the Gluck twist in , related to Kirby problem 4.23. |
Keywords
$4$–manifold, knot, surface, diagram
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Mathematical Subject Classification
Primary: 57K45
Secondary: 57K40
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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
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Authors |
| Mark C Hughes | |
| Department of Mathematics Brigham Young University Provo, UT United States |
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| https://math.byu.edu/~hughes/ | |
| Seungwon Kim | |
| Center for Geometry and
Physics Institute for Basic Science (IBS) Pohang South Korea |
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| https://sites.google.com/view/seungwonkim | |
| Maggie Miller | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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| https://web.math.princeton.edu/~maggiem | |
