Chern character for twisted complexes

We construct a Chern character of a perfect complex of twisted modules over an algebroid stack

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.Comment: 33 page

Deligne groupoid revisited

We show that for a differential graded Lie algebra $\mathfrak{g}$ whose components vanish in degrees below -1 the nerve of the Deligne 2-groupoid is homotopy equivalent to the simplicial set of $\mathfrak{g}$-valued differential forms introduced by V.Hinich

Formality theorem for gerbes

We extend the formality theorem of Maxim Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes on smooth and complex manifolds.Comment: arXiv admin note: substantial text overlap with arXiv:0903.184

Femtosecond X-ray emission study of the spin cross-over dynamics in haem proteins

In haemoglobin (consisting of four globular myoglobin-like subunits), the change from the low-spin (LS) hexacoordinated haem to the high spin (HS) pentacoordinated domed form upon ligand detachment and the reverse process upon ligand binding, represent the transition states that ultimately drive the respiratory function. Visible-ultraviolet light has long been used to mimic the ligand release from the haem by photodissociation, while its recombination was monitored using time-resolved infrared to ultraviolet spectroscopic tools. However, these are neither element- nor spin-sensitive. Here we investigate the transition state in the case of Myoglobin-NO (MbNO) using femtosecond Fe Kalpha and Kbeta non-resonant X-ray emission spectroscopy (XES) at an X-ray free-electron laser upon photolysis of the Fe-NO bond. We find that the photoinduced change from the LS (S = 1/2) MbNO to the HS (S = 2) deoxy-myoglobin (deoxyMb) haem occurs in ca. 800 fs, and that it proceeds via an intermediate (S = 1) spin state. The XES observables also show that upon NO recombination to deoxyMb, the return to the planar MbNO ground state is an electronic relaxation from HS to LS taking place in ca. 30 ps. Thus, the entire ligand dissociation-recombination cycle in MbNO is a spin cross-over followed by a reverse spin cross-over process

Oscilatory modules

Developing the ideas of Bressler and Soibelman and of Karabegov, we introduce a notion of an oscillatory module on a symplectic manifold which is a sheaf of modules over the sheaf of deformation quantization algebras with an additional structure. We compare the category of oscillatory modules on a torus to the Fukaya category as computed by Polishchuk and Zaslow.Comment: To appear in the proceedings of Moshe Flato Memorial Conference, November, 2008, Ben Gurion Universit