An obstruction to sliceness via contact geometry and ?classical? gauge theory

Rudolph, Lee

doi:10.1007/bf01245177

Cited by 64 publications

(74 citation statements)

References 13 publications

(16 reference statements)

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“…Since the Rasmussen invariant of the 2-component unlink is 1, it follows that such a Bing double is not smoothly slice. This latter statement can also be obtained from results of L Rudolph [19]. Nevertheless, our computations show that this fact follows very easily from elementary properties of the Rasmussen invariant.…”

Section: Introductionsupporting

confidence: 46%

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Slicing Bing doubles

Cimasoni

2006

Algebr. Geom. Topol.

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Bing doubling is an operation which produces a 2-component boundary link B(K) from a knot K. If K is slice, then B(K) is easily seen to be boundary slice. In this paper, we investigate whether the converse holds. Our main result is that if B(K) is boundary slice, then K is algebraically slice. We also show that the Rasmussen invariant can tell that certain Bing doubles are not smoothly slice.Comment: This is the version published by Algebraic & Geometric Topology on 13 December 200

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Section: Introductionsupporting

confidence: 46%

“…This statement is by no means new. Indeed, L Rudolph [19] showed that if TB.K/ 0, then Wh.K/ is not smoothly slice. By the cobordism illustrated in Figure 5, this implies that B.K/ is not smoothly slice.…”

Section: Boundary Sliceness Of Bing Doublesmentioning

confidence: 99%

Slicing Bing doubles

Cimasoni

2006

Algebr. Geom. Topol.

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“…X whose boundary is a Legendrian knot K 2 L. Then Lisca and Matić's adjunction inequality ( [17], and [19] for X D D 4 ) gives:…”

Section: Lagrangian Surfaces In Stein Fillingmentioning

confidence: 99%

Lagrangian concordance of Legendrian knots

Chantraine

2010

Algebr. Geom. Topol.

119

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In this article we define Lagrangian concordance of Legendrian knots, the analogue of smooth concordance of knots in the Legendrian category. In particular we study the relation of Lagrangian concordance under Legendrian isotopy. The focus is primarily on the algebraic aspects of the problem. We study the behavior of the classical invariants under this relation, namely the Thurston-Bennequin number and the rotation number, and we provide some examples of non-trivial Legendrian knots bounding Lagrangian surfaces in $D^4$. Using these examples, we are able to provide a new proof of the local Thom conjecture.Comment: 18 pages, 4 figures. v2: Minor corrections and a proof of conjecture 6.4 of version 1 (now Theorem 6.4). v3: Several substantial changes notably the proof of theorems 1.2 and 5.1, this is the version accepted for publication in "Algebraic and Geometric Topology" published in January 201

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“…[9], [11]. In order to have the standard orientation on R 3 , we note that the positive y-axis goes into the page.…”

Section: Front Projection and Arc Presentationmentioning

confidence: 99%