Configuration spaces are not homotopy invariant

We present a counterexample to the conjecture on the homotopy invariance of configuration spaces. More precisely, we consider the lens spaces $L_{7,1}$ and $L_{7,2}$, and prove that their configuration spaces are not homotopy equivalent by showing that their universal coverings have different Massey products.Comment: 6 page

Associative algebras, punctured disks and the quantization of Poisson manifolds

The aim of the note is to provide an introduction to the algebraic, geometric and quantum field theoretic ideas that lie behind the Kontsevich-Cattaneo-Felder formula for the quantization of Poisson structures. We show how the quantization formula itself naturally arises when one imposes the following two requirements to a Feynman integral: on the one side it has to reproduce the given Poisson structure as the first order term of its perturbative expansion; on the other side its three-point functions should describe an associative algebra. It is further shown how the Magri-Koszul brackets on 1-forms naturally fits into the theory of the Poisson sigma-model.Comment: LaTeX, 8 pages, uses XY-pic. Few typos corrected. Final versio

On the Hochschild-Kostant-Rosenberg map for graded manifolds

We show that the Hochschild-Kostant-Rosenberg map from the space of multivector fields on a graded manifold N (endowed with a Berezinian volume) to the cohomology of the algebra of multidifferential operators on N (as a subalgebra of the Hochschild complex of the algebra of smooth functions on N) is an isomorphism of Batalin-Vilkovisky algebras. These results generalize to differential graded manifolds.Comment: 15 pages. Problematic Lemma 5.5 of v1 removed and Theorem 5.3b corrected accordingly. Exposition reorganized. To appear in IMR

Nontrivial classes in H∗(Imb(S1,Rn))H^*(Imb(S^1,\R^n)) from nontrivalent graph cocycles

We construct nontrivial cohomology classes of the space $Imb(S^1,\R^n)$ of imbeddings of the circle into $\R^n$, by means of Feynman diagrams. More precisely, starting from a suitable linear combination of nontrivalent diagrams, we construct, for every even number $n\geq 4$, a de Rham cohomology class on $Imb(S^1,\R^n)$. We prove nontriviality of these classes by evaluation on the dual cycles.Comment: 10 pages, 11 figures. V2: minor changes, typos correcte

Algebraic structures on graph cohomology

We define algebraic structures on graph cohomology and prove that they correspond to algebraic structures on the cohomology of the spaces of imbeddings of S^1 or R into R^n. As a corollary, we deduce the existence of an infinite number of nontrivial cohomology classes in Imb(S^1,R^n) when n is even and greater than 3. Finally, we give a new interpretation of the anomaly term for the Vassiliev invariants in R^3.Comment: Typos corrected, exposition improved. 14 pages, 2 figures. To appear in J. Knot Theory Ramification

Configuration spaces and Vassiliev classes in any dimension

The real cohomology of the space of imbeddings of S^1 into R^n, n>3, is studied by using configuration space integrals. Nontrivial classes are explicitly constructed. As a by-product, we prove the nontriviality of certain cycles of imbeddings obtained by blowing up transversal double points in immersions. These cohomology classes generalize in a nontrivial way the Vassiliev knot invariants. Other nontrivial classes are constructed by considering the restriction of classes defined on the corresponding spaces of immersions.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-39.abs.htm

Comparative life cycle assessment of Fe2O3-based fibers as anode materials for sodium-ion batteries

AbstractSodium-ion batteries (SIBs) potentially represent a more sustainable, less expensive and environmentally friendly alternative to lithium-ion batteries. The development of new low-cost, non-toxic, highly performing electrode materials is the key point for the SIB technology advances. This study develops a basic life cycle assessment (LCA) model for the evaluation of the production by electrospinning of iron (III) oxide-based fibers to be used as anode materials in SIBs. Indeed, it has been recently demonstrated that electrospun silicon-doped iron (III) oxide (Fe2O3) fibers exhibit outstanding electrochemical properties and gravimetric capacities never achieved before for pure Fe2O3-based anodes. The LCA methodology is utilized in order to analyze the environmental burdens (from raw material extraction to manufacturing process) of these electrode materials. The simplified comparative LCA studies, conducted to assess the environmental impacts associated with the electrospun Fe2O3 and Fe2O3:Si fibers at the same cell performance, demonstrate that the Si-doped anode material, which exhibits better electrochemical performance with respect to the undoped one, has also lower impact for each category of damage, namely human health, ecosystem quality and resources

An Integrated Theoretical/Experimental Study of Quinolinic-Isoquinolinic Derivatives Acting as Reversible Electrochromes

A series of compounds, featuring an ethenylic bridge and quinoline and isoquinoline end capping units possessing systematically varied substitution patterns, were prepared as molecular materials for electrochromic applications. The different structures were optimized in order to maximize the electrochromic contrast in the visible region, mostly by achieving a completely UV-absorbing oxidized state. Density functional theory (DFT) calculations are exploited in order to rationalize the correlation between the molecular structure, the functional groups' electronic properties, and the electrochemical behavior. It is shown that the molecular planarity (i.e. ring/ring pi conjugation) plays a major role in defining the mechanism of the electrochemical charge transfer reaction, while the substituent's nature has an influence on the LUMO energy. Among the compounds here studied, the (E)-10-methyl-9-(2-(2-methylisoquinolinium1- yl)-vinyl)-1,2,3,4-tetrahydroacri-dinium trifluoromethanesulfonate derivative shows the most interesting properties as an electrochromophore