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1 Introduction From its first introduction in [14], the Jones polynomial has played a decisive role in knot theory. This invariant κ → V κ associates to an oriented link κ ⊂ S 3 a Laurent polynomial in t 1/2. It is completely characterised by V unknot = 1 and a relation obtained from the Kauffman bracket calculus, which allows one to successively reduce the(More)
We present a new proof of a result due to Taubes: if (X, ω) is a closed symplectic four-manifold with b+(X) > 1 + b1(X) and λ[ω] ∈ H 2 (X; Q) for some λ ∈ R + , then the Poincaré dual of KX may be represented by an embedded symplectic submanifold. The result builds on the existence of Lefschetz pencils on symplectic four-manifolds. We approach the(More)
We describe various approaches to understanding Fukaya categories of cotangent bundles. All of the approaches rely on introducing a suitable class of noncompact Lagrangian submanifolds. We review the work of Nadler-Zaslow [28, 27] and the authors [14], before discussing a new approach using family Floer cohomology [10] and the " wrapped Fukaya category ".(More)
Sixty-four samples from six grade 4 astrocytomas were investigated ex vivo by 1H MRS at 360 MHz and subsequently by histopathology to obtain percentages of viable and necrotic tumour and grey and white matter. MR-visible lipids were detected in 87% of tumour samples. Necrotic foci were < 3 x 3 x 6 mm3. The means of the intensities/unit weight tissue of the(More)
The application of 13C-nuclear magnetic resonance spectroscopy to the structural determination of the capsular polysaccharide antigens of Neisseria meningitidis is described. Complete assignments of the spectra of the polysaccharides of serogroups A, B, C, W-135, X and Y were made and were based mainly on previous assignments made for the monomer units of(More)
The interaction of the local anesthetic tetracaine with phosphatidylserine-containing model membranes has been studied by 2H-NMR. Charged tetracaine exhibited an unusually large partition coefficient into multilamellar dispersions of phosphatidylserine. The 2H-NMR spectra consisted of a Pake doublet and a narrow line, with the former corresponding to(More)
The interactions of the local anesthetic tetracaine with multilamellar dispersions of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and cholesterol have been investigated by deuterium nuclear magnetic resonance of specifically deuteriated tetracaines, DMPC and cholesterol. Experiments were performed at pH 5.5, when the anesthetic is primarily charged,(More)