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Kim, Seungwon
기하학 수리물리 연구단
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Isotopies of surfaces in 4–manifolds via banded unlink diagrams

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Title
Isotopies of surfaces in 4–manifolds via banded unlink diagrams
Author(s)
Hughes, M.C.; Seungwon Kim; Miller, M.
Subject
4–manifold, knot, surface, diagram
Publication Date
2020-09
Journal
GEOMETRY & TOPOLOGY, v.24, no.3, pp.1519 - 1569
Publisher
GEOMETRY & TOPOLOGY PUBLICATIONS
Abstract
© 2020, Mathematical Sciences Publishers. 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 CP2 (ie spheres in the generating homology class), proving that many explicit unit surfaces are isotopic to the standard CP1. This strengthens some previously known results about the Gluck twist in S4, related to Kirby problem 4.23
URI
https://pr.ibs.re.kr/handle/8788114/7635
DOI
10.2140/gt.2020.24.1519
ISSN
1465-3060
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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