Realizing modules over the homology of a DGA

Let A be a DGA over a field and X a module over H_*(A). Fix an $A_\infty$-structure on H_*(A) making it quasi-isomorphic to A. We construct an equivalence of categories between A_{n+1}-module structures on X and length n Postnikov systems in the derived category of A-modules based on the bar resolution of X. This implies that quasi-isomorphism classes of A_n-structures on X are in bijective correspondence with weak equivalence classes of rigidifications of the first n terms of the bar resolution of X to a complex of A-modules. The above equivalences of categories are compatible for different values of n. This implies that two obstruction theories for realizing X as the homology of an A-module coincide.Comment: 24 page

Collinear versus non-collinear magnetic order in Pd atomic clusters: ab-initio calculations

We present a thorough theoretical assessment of the stability of non-collinear spin arrangements in small palladium clusters. We generally find that ferromagnetic order is always preferred, but that antiferromagnetic and non-collinear configurations of different sorts exist and compete for the first excited isomers. We also show that the ground state is insensitive to the choice of atomic configuration for the pseudopotential used and to the approximation taken for the exchange and correlation potential. Moreover, the existence and relative stability of the different excited configurations also depends weakly on the approximations employed. These results provide strong evidence on the transferability of pseudopotential and exchange and correlation functionals for palladium clusters as opposed to the situation found for the bulk phases of palladium.Comment: 5 pages, 4 figure

An Array of Layers in Silicon Sulfides: Chain-like and Ground State Structures

While much is known about isoelectronic materials related to carbon nanostructures, such as boron nitride layers and nanotubes, rather less is known about equivalent silicon based materials. Following the recent discovery of phosphorene, we herein discuss isoelectronic silicon monosulfide monolayers. We describe a set of anisotropic ground state structures that clearly have a high stability with respect to the near isotropic silicon monosulfide monolayers. The source of the layer anisotropy is related to the presence of Si-S double chains linked by some Si-Si covalent bonds, which lye at the core of the increased stability, together with a remarkable spd hybridization on Si. The involvement of d orbitals brings more variety to silicon-sulfide based nanostructures that are isoelectronic to phosphorene, which could be relevant for future applications, adding extra degrees of freedom.Comment: 16 pages, 6 figure

Givental's non-linear Maslov index on lens spaces

Givental's non-linear Maslov index, constructed in 1990, is a quasimorphism on the universal cover of the identity component of the contactomorphism group of real projective space. This invariant was used by several authors to prove contact rigidity phenomena such as orderability, unboundedness of the discriminant and oscillation metrics, and a contact geometric version of the Arnold conjecture. In this article we give an analogue for lens spaces of Givental's construction and its applications.Comment: 44 pages; v3: minor changes; v2: besides minor changes, we corrected a mistake in Corollary 1.3(iv

Substitutional 4d and 5d Impurities in Graphene

We describe the structural and electronic properties of graphene doped with substitutional impurities of 4d and 5d transition metals. The binding energy and distances for 4d and 5d metals in graphene show similar trends for the later groups in the periodic table, which is also well-known characteristic of 3d elements. However, along earlier groups the 4d impurities in graphene show very similar binding energies, distances and magnetic moments to 5d ones, which can be related to the influence of the 4d and 5d lanthanide contraction. Surprisingly, within the manganese group, the total magnetic moment of 3$\mu_{B}$ for manganese is reduced to 1$\mu_{B}$ for technetium and rhenium. We find that with compared with 3d elements, the larger size of the 4d and 5d elements causes a high degree hybridization with the neighbouring carbon atoms, reducing spin splitting in the d levels. It seems that the magnetic adjustment of graphene could be significantly different is 4d or 5d impurities are used instead of 3d impurities.Comment: 16 pages, 4 figure