The relative Whitney trick and its applications

Davis, Chelsea S.; Orson, Patrick; Park, JungHwan

doi:10.1007/s00029-021-00738-y

Cited by 1 publication

(4 citation statements)

References 19 publications

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“…In order to the Whitney tower of Theorem 1.2, we pass through an object called a relative Whitney tower. These are introduced in [DOP22] where they are used to transform an immersed union of disks bounded by a link K into a sequence of crossing changes from K to a new link bounding a disjoint union of immersed disks. In Section 3 we define symmetric relative Whitney towers and explain how to construct symmetric Whitney towers from them.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

“…We delay its proof until the end of the section. Lemma 4.2 (Compare to Lemma 5.4 [DOP22]). Let W be a 4-manifold with boundary.…”

Section: Symmetric Relative Whitney Towersmentioning

confidence: 99%

“…Symmetric Whitney towers are a restriction of a larger class of immersed 2-complexes in 4-manifolds, simply called Whitney towers. In [DOP22] the author along with Orson and Park define a variation of a Whitney tower called a relative Whitney tower. Relative Whitney towers have two important properties.…”

Section: Symmetric Relative Whitney Towersmentioning

confidence: 99%

“…By performing the partial relative Whitney move on all of the relative Whitney disks of T one gets a symmetric Whitney tower. Lemma 3.2 (Compare to Lemma 5.5 of [DOP22]). Let W be a 4-manifold and T be a height h symmetric relative Whitney tower in W .…”

Section: Symmetric Relative Whitney Towersmentioning

confidence: 99%

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Concordance, Crossing Changes, and Knots in Homology Spheres

Davis¹

2019

Can. Math. Bull.

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Any knot in S 3 may be reduced to a slice knot by crossing changes. Indeed, this slice knot can be taken to be the unknot. In this paper we study the question of when the same holds for knots in homology spheres. We show that a knot in a homology sphere is nullhomotopic in a smooth homology ball if and only if that knot is smoothly concordant to a knot which is homotopic to a smoothly slice knot. As a consequence, we prove that the equivalence relation on knots in homology spheres given by cobounding immersed annuli in a homology cobordism is generated by concordance in homology cobordisms together with homotopy in a homology sphere.

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Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

“…We delay its proof until the end of the section. Lemma 4.2 (Compare to Lemma 5.4 [DOP22]). Let W be a 4-manifold with boundary.…”

Section: Symmetric Relative Whitney Towersmentioning

confidence: 99%

Section: Symmetric Relative Whitney Towersmentioning

confidence: 99%

Section: Symmetric Relative Whitney Towersmentioning

confidence: 99%

See 2 more Smart Citations