Braids,mapping class groups,and categorical delooping

Dehn twists around simple closed curves in oriented surfaces satisfy the braid relations. This gives rise to a group theoretic map from the braid group to the mapping class group. We prove here that this map is trivial in homology with any trivial coefficients in degrees less than g/2. In particular this proves an old conjecture of J. Harer. The main tool is categorical delooping in the spirit of (Tillmann in Invent Math 130:257–175, 1997). By extending the homomorphism to a functor of monoidal 2-categories, is seen to induce a map of double loop spaces on the plus construction of the classifying spaces. Any such map is null-homotopic. In an appendix we show that geometrically defined homomorphisms from the braid group to the mapping class group behave similarly in stable homology. The first author was supported by Inha University research grant.     

Degenerations of ideal hyperbolic triangulations

Let M be a cusped 3-manifold, and let ${\mathcal{T}}$ be an ideal triangulation of M. The deformation variety ${\mathfrak{D}(\mathcal{T})}$ , a subset of which parameterises (incomplete) hyperbolic structures obtained on M using ${\mathcal{T}}$ , is defined and compactified by adding certain projective classes of transversely measured singular codimension-one foliations of M. This leads to a combinatorial and geometric variant of well-known constructions by Culler, Morgan and Shalen concerning the character variety of a 3-manifold.     

Extrinsic homogeneity of parallel submanifolds

We consider parallel submanifolds M of a Riemannian symmetric space N and study the question whether M is extrinsically homogeneous in N, i.e. whether there exists a subgroup of the isometry group of N which acts transitively on M. Provided that N is of compact or non-compact type, we establish the extrinsic homogeneity of every complete irreducible parallel submanifold of N whose dimension is at least three and which is not contained in any flat of N.     

Tetrahalidometallate(II) Ionic Liquids with More than One Metal: The Effect of Bromide versus Chloride

Fifteen N-butylpyridinium salts – five monometallic [C₄Py]₂[MBr₄] and ten bimetallic [C₄Py]₂[M_0.5^aM_0.5^bBr₄] (M=Co, Cu, Mn, Ni, Zn) – were synthesized, and their structures and thermal and electrochemical properties were studied. All the compounds are ionic liquids (ILs) with melting points between 64 and 101 °C. Powder and single-crystal X-ray diffraction show that all ILs are isostructural. The electrochemical stability windows of the ILs are between 2 and 3 V. The conductivities at room temperature are between 10⁻⁵ and 10⁻⁶ S cm⁻¹. At elevated temperatures, the conductivities reach up to 10⁻⁴ S cm⁻¹ at 70 °C. The structures and properties of the current bromide-based ILs were also compared with those of previous examples using chloride ligands, which illustrated differences and similarities between the two groups of ILs.     

Gating the mechanistic pathway to the elusive 4-membered ring azeteoporphyrin

Photolysis of metalated (Cu and Ni) and free base 2-diazo-3-oxochlorins within a frozen matrix (λ = 457.9 nm, toluene, 80 K) generates a single photointermediate with a hypsochromically shifted electronic absorption spectrum relative to the starting diazochlorins. The appearance of ketene (~2131 cm(-1)) and azete (~1670 cm(-1)) vibrations in infrared absorption and Raman spectra, respectively, identifies this intermediate as resulting from the Wolff rearrangement of the diazochlorins upon N(2) loss. Computational modeling of the vibrational spectra and TDDFT simulation of the electronic transitions of potential photointermediates corroborate this assignment. Isolation and analysis of photoproducts of these diazochlorins formed within n-butanol-doped frozen toluene matrices indicate near exclusive formation of azeteoporphyrins. In sharp contrast, room temperature laser photolysis of these materials yields a mixture of photoproducts deriving from the presence of both carbene and ketene intermediates. Computational modeling of the intramolecular reactivity of the proposed sp(2) carbene intermediate shows exclusive bond insertion to the adjacent phenyl group, and no evidence of Wolff rearrangement. Computational reaction profile analyses reveal that the barrierless Wolff rearrangement proceeds via an out-of-plane carbene electronic configuration that is generated directly during the loss of N(2). The formation of out-of-plane carbene, resulting in the exclusive formation of the observed ketene photointermediate at low temperatures, is consistent with orbital symmetry considerations and by the geometric constraints imposed by the frozen matrix. Combined, this leads to a model showing that azeteoporphyrin formation via the Wolff rearrangement is dependent upon the structural disposition of the adjacent framework, and the specific reaction intermediate formed is very sensitive to this feature.     

Spherical aberration correction in tandem with exit-plane wave function reconstruction: interlocking tools for the atomic scale imaging of lattice defects in GaAs.

With the availability of resolution boosting and delocalization minimizing techniques, for example, spherical aberration correction and exit-plane wave function reconstruction, high-resolution transmission electron microscopy is drawing to a breakthrough with respect to the atomic-scale imaging of common semiconductor materials. In the present study, we apply a combination of these two state-of-the-art techniques to investigate lattice defects in GaAs-based heterostructures at atomic resolution. Focusing on the direct imaging of stacking faults as well as the core structure of edge and partial dislocations, the practical capabilities of both techniques are illustrated. For the first time, we apply the technique of bright-atom contrast imaging at negative spherical aberration together with an appropriate overfocus setting for the investigation of lattice defects in a semiconductor material. For these purposes, the elastic displacements associated with lattice defects in GaAs viewed along the 110 zone axis are measured from experimental images using reciprocal space strain map algorithms. Moreover, we demonstrate the benefits of the retrieval of the exit-plane wave function not only for the elimination of residual imaging artefacts but also for the proper on-line alignment of specimens during operation of the electron microscope--a basic prerequisite to obtain a fair agreement between simulated images and experimental micrographs.     

Vergleichende Untersuchungen zur Struktur von 4‐Dimethylaminopyridin‐Addukten

Comparative Structural Studies on 4‐Dimethylaminopyridine‐Adducts Lewis acid‐base adducts of the type dmap—MMe₃ (M = Al 1 , Ga 2 , In 3 , Tl 4 ) as well as dmap—AlCl₃ ( 6 ) and dmap—Al(t‐Bu)₃ ( 7 ) were synthesized by reaction of MR₃ with 4‐dimethylamino‐pyridine (dmap) whereas dmap—AlH₃ ( 5 ) was obtained from AlH₃·Et₂O. 1 — 7 were characterized by means of NMR (¹H, ¹³C{¹H}) and mass spectrometry and elemental analysis. In addition, their solid state structures were determined by single crystal X‐ray diffraction studies. A comparison of the structural parameters reveales the influence of both electronic (Lewis acidity of the group 13 atom) and steric interactions on the structure and stability of as prepared Lewis acid‐base adducts.     

Mesoionic bora-tetraazapentalenes--fully reversible two step redox systems

Bora-tetraazapentalenes have been synthesised and characterized; the radical anion shows an unusual thermodynamic stability (semiquinone formation constants K(SEM) of ca. 10(14)).