Exotic structures and adjunction inequality

By S. Akbulut, R. Matveyev. 2000

74 citations recorded by the source corpus.

We reprove and strengthen some old difficult theorems of 4-manifolds by the aid of recently discovered modern tools, which involve contact structures on 3-manifolds, compact Stein domains, etc.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2d381ab219e3bc403b8cc2ed4be232f5aebaddd6

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Bounds for the Thurston–Bennequin number from Floer homology (2003, background): “ing one of the two crossings in the cusp connecting the two copies of the knot. Then the unknotting number for a Whitehead double cannot be greater than one. Now, by a theorem of Akbulut and Matveyev [AM] the knot K n has a Legendrian representative L n with tb(L n) = 1 provided that the original kn”
A Survey of Classical Knot Concordance (2003, methodology): “…techniques to the study of smooth 4–manifolds, beginning with the work of Donaldson [20] [21] and including the introduction of Seiberg–Witten invariants and their application to symplectic manifolds, the use of the Thurston–Bennequin invariant [2] [99], and recent work of Ozsváth and Szabó [94].”
Legendrian and Transversal Knots (2003, background): “3 (Akbulut and Matveyev 1997, [2]; Lisca and Matic 1998, [64]).”
A concordance invariant from the Floer homology of double branched covers (2005, unknown): “(See also [1], [17] for different proofs.”
Knot Floer homology of Whitehead doubles (2006, background): “ologically slice. While it is easy to see that the Whitehead double of a smoothly slice knot is also smoothly slice, it was shown by several authors that many Whitehead doubles are not smoothly slice [1, 8, 39]. The existence of a topologically slice knot which is not smoothly slice is interesting i”