6,683 research outputs found
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 .
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
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