In this lecture, delivered at the string theory and geometry workshop in Oberwolfach, we review some of the concepts of generalized geometry, as introduced by Hitchin and developed in the speaker’s thesis. We also prove a Hodge decomposition for the twisted cohomology of a compact generalized Kähler manifold, as well as a generalization of the dd-lemma of Kähler geometry. 1 Geometry of T ⊕ T ∗ ...

The purpose of this paper is to complete Getzler-Jones’ proof of Deligne’s Conjecture, thereby establishing an explicit relationship between the geometry of configurations of points in the plane and the Hochschild complex of an associative algebra. More concretely, it is shown that the B∞-operad, which is generated by multilinear operations known to act on the Hochschild complex, is a quotient ...

Let A be one of the following commutative associative algebras: the algebra of all smooth functions on the plane: A = C(R), or the algebra of polynomials A = C[p, q] over R or C. There exists a non-trivial formal associative deformation of A called the Moyal ⋆-product (or the standard ⋆-product). It is defined as an associative operation A → A[[h̄]] where h̄ is a formal variable. The explicit for...

We introduce diagrams and Reidemeister moves for links in F ×S, where F is an orientable surface. Using these diagrams we compute (in a new way) the Kauffman Bracket Skein Modules (KBSM ) for D × S and A× S, where D is a disk and A is an annulus. Moreover, we also find the KBSM for the F0,3 × S , where F0,3 denotes a disk with two holes, and thus show that the module is free.

In symplectic geometry, it is often useful to consider the so-called Poisson bracket on the algebra of functions on a C ∞ symplectic manifold M. The bracket determines, and is determined by, the symplectic form; however, many of the features of symplectic geometry are more conveniently described in terms of the Poisson bracket. When one turns to the study of symplectic manifolds in the holomorp...

In any 2-category C with zeros (for example the topological 2-category T op∗ of based spaces, based maps and track classes of homotopies) box bracket operations have been defined and studied by Hardie-Marcum-Oda [4]. These are secondary homotopy operations and if (as we will suppose) C admits a suspension functor Σ (see [3]) they take values in morphism groups HC(ΣW,X), here denoted π(ΣW,X), of...

Background. Any decrease in friction between orthodontic wire and bracket can accelerate tooth movement in the sliding technique and result in better control of anchorage. This study was carried out to evaluate frictional forces by coating orthodontic wires and porcelain brackets with zinc oxide nanoparticles (ZnO). Methods . In this in vitro study, we evaluated a combination of 120 samples of ...

A clinical trial was carried out to evaluate and compare the clinical performance of a visible light-cured material with a chemically cured adhesive. This was used in combination with two types of bracket base. Fifty-two patients entered the trial and 542 bracket bases were placed. The incidence and site of bond failure were recorded. The overall failure rate for the light-cured material in com...

After 20 months of clinical testing and more than 600 bonded arches, brief interim conclusions can be drawn on treatment with a new lingual bracket system, one that differs fundamentally from conventional appliances in both design and manufacture. The demand for maximum individuality is met by using state-of-the-art computer-aided design/computer-aided manufacturing technology to fuse the 2 nor...

A new method to derive presentations of skein modules is developed. For the case of homotopy skein modules it will be shown how the topology of a 3-manifold is reflected in the structure of the module. The freeness problem for q-homotopy skein modules is solved, and a natural skein module related to linking numbers is computed.