Floer theory for negative line bundles via Gromov-Witten invariants

Let M be the total space of a negative line bundle over a closed symplectic manifold. We prove that the quotient of quantum cohomology by the kernel of a power of quantum cup product by the first Chern class of the line bundle is isomorphic to symplectic cohomology. We also prove this for negative vector bundles and the top Chern class. We explicitly calculate the symplectic and quantum cohomologies of O(-n) over P^m. For n=1, M is the blow-up of C^{m+1} at the origin and symplectic cohomology has rank m. The symplectic cohomology vanishes if and only if the first Chern class of the line bundle is nilpotent in quantum cohomology. We prove a Kodaira vanishing theorem and a Serre vanishing theorem for symplectic cohomology. In general, we construct a representation of \pi_1(Ham(X,\omega)) on the symplectic cohomology of symplectic manifolds X conical at infinity.Comment: 53 pages; version 3: improved discussion of maximum principle for negative vector bundles. The final version is published in Advances in Mathematic

Surgical concepts for reconstruction of the auricle

We compiled and evaluated the world literature on auricular reconstruction, for a total of over 400 publications, more than 200 authors, and over 3,300 reported cases. We found that partial reconstructions were already performed as early as 600 BC; total reconstructions were still considered impracticable in 1830. But since 1891, more than 40 different cartilaginous, osseous, and alloplastic frame materials have been described. Only eight of these were still being applied in the last decade, with autogenous costal cartilage and silicone as the leading substances. Results of the operation can be improved by special surgical manipulations, eg, the "fan-flap" technique. Taking into consideration the complication rate, the number of individual interventions, and the stability of the results, we devised a special point system that makes possible a limited assessment of the different surgical techniques

Conformal Bootstrap With Slightly Broken Higher Spin Symmetry

We consider conformal field theories with slightly broken higher spin symmetry in arbitrary spacetime dimensions. We analyze the crossing equation in the double light-cone limit and solve for the anomalous dimensions of higher spin currents $\gamma_s$ with large spin $s$. The result depends on the symmetries and the spectrum of the unperturbed conformal field theory. We reproduce all known results and make further predictions. In particular we make a prediction for the anomalous dimensions of higher spin currents in the 3d Ising model.Comment: 41 pages, 2 figures, %\draftmod