Dissolving four-manifolds and positive scalar curvature

We prove that many simply connected symplectic four-manifolds dissolve after connected sum with only one copy of $S^{2}\times S^{2}$. For any finite group G that acts freely on the three-sphere we construct closed smooth four-manifolds with fundamental group G which do not admit metrics of positive scalar curvature, but whose universal covers do admit such metrics.Comment: 13 pages; to appear in Mathematische Zeitschrif

Coarse topology, enlargeability, and essentialness

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K-theory of the corresponding reduced C*-algebras. Our proofs do not depend on the Baum--Connes conjecture and provide independent confirmation for specific predictions derived from this conjecture.Comment: 21 pages, 2 figures. Revised version. To appear in Ann. Sci. Ecole Norm. Su

The strong Novikov conjecture for low degree cohomology

We show that for each discrete group G, the rational assembly map K_*(BG) \otimes Q \to K_*(C*_{max} G) \otimes \Q is injective on classes dual to the subring generated by cohomology classes of degree at most 2 (identifying rational K-homology and homology via the Chern character). Our result implies homotopy invariance of higher signatures associated to these cohomology classes. This consequence was first established by Connes-Gromov-Moscovici and Mathai. Our approach is based on the construction of flat twisting bundles out of sequences of almost flat bundles as first described in our previous work. In contrast to the argument of Mathai, our approach is independent of (and indeed gives a new proof of) the result of Hilsum-Skandalis on the homotopy invariance of the index of the signature operator twisted with bundles of small curvature.Comment: 11 page

Modified critical correlations close to modulated and rough surfaces

Correlation functions are sensitive to the presence of a boundary. Surface modulations give rise to modified near surface correlations, which can be measured by scattering probes. To determine these correlations, we develop a perturbative calculation in deformations in height from a flat surface. The results, combined with a renormalization group around four dimensions, are also used to predict critical behavior near a self-affinely rough surface. We find that a large enough roughness exponent can modify surface critical behavior.Comment: 4 pages, 1 figure. Revised version as published in Phys. Rev. Lett. 86, 4596 (2001

Synthesis of atomically thin hexagonal boron nitride films on nickel foils by molecular beam epitaxy

Hexagonal boron nitride (h-BN) is a layered two-dimensional material with properties that make it promising as a dielectric in various applications. We report the growth of h-BN films on Ni foils from elemental B and N using molecular beam epitaxy. The presence of crystalline h-BN over the entire substrate is confirmed by Raman spectroscopy. Atomic force microscopy is used to examine the morphology and continuity of the synthesized films. A scanning electron microscopy study of films obtained using shorter depositions offers insight into the nucleation and growth behavior of h-BN on the Ni substrate. The morphology of h-BN was found to evolve from dendritic, star-shaped islands to larger, smooth triangular ones with increasing growth temperature