The relative Whitney trick and its applications

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We introduce a geometric operation, which we call the relative Whitney trick, that removes a single double point between properly immersed surfaces in a 4-manifold with boundary.Using the relative Whitney trick we prove that every link in a homology sphere is homotopic to a link that is topologically slice in a contractible topological 4-manifold. We further prove that any link in a homology sphere is order k Whitney tower concordant to a link in S-3 for all k. Finally, we explore the minimum Gordian distance from a link in S-3 to a homotopically trivial link. Extending this notion to links in homology spheres, we use the relative Whitney trick to make explicit computations for 3-component links and establish bounds in general.
Publisher
SPRINGER INT PUBL AG
Issue Date
2022-05
Language
English
Article Type
Article
Citation

SELECTA MATHEMATICA-NEW SERIES, v.28, no.2

ISSN
1022-1824
DOI
10.1007/s00029-021-00738-y
URI
http://hdl.handle.net/10203/291698
Appears in Collection
MA-Journal Papers(저널논문)
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