Many papers have been devoted recently to twisted K-theory as originally defined in [15] and [29]. See for instance the references [2], [23] and the very accessible paper [30]. We offer here a more direct approach based on the notion of “twisted vector bundles”. This is not an entirely new idea, since we find it in [4], [6], [7], [8] and [9] for instance, under different names and from various ...

An important property of electromagnetic fields, which arises from the interaction between fields and chiral molecules, is called optical chirality. By enhancing this field property, while maintaining constant input power, we are able to increase absorption of circularly polarized light by chiral molecules of a certain handedness. This enhancement is achieved through the use of achiral plasmoni...

We consider the neutron star (NS) of the magnetar type inside the massive binary system. We determine the conditions under which the matter from the stellar wind can penetrate the inner magnetosphere of the magnetar. At some distance from the NS surface, the magnetic pressure can balance the gravitational pressure of the accreting matter creating very turbulent, magnetized transition region. It...

The twisted cube TQn is an alternative to the popular hypercube network. Recently, some interesting properties of TQn were investigated. In this paper, we study the pancycle problem on faulty twisted cubes. Let fe and fv be the numbers of faulty edges and faulty vertices in TQn, respectively. We show that, with fe + fv 6 n 2, a faulty TQn still contains a cycle of length l for every 4 6 l 6 jV(...

Yoshida in [6] and Tillmann in [3] describe di erent methods of producing surfaces within a 3-manifoldM with boundary from ideal points of the deformation variety of M , given a particular ideal tetrahedralisation of M . The Yoshida construction builds a surface from twisted squares within the tetrahedra, the Tillmann construction results in a spun-normal surface relative to the tetrahedra. In ...

We introduce the notion of “local system of ZT -twisted vertex operators” on a Z2-graded vector space M , generalizing the notion of local system of vertex operators [Li]. First, we prove that any local system of ZT -twisted vertex operators on M has a vertex superalgebra structure with an automorphism σ of order T with M as a σ-twisted module. Then we prove that for a vertex (operator) superal...

D-branes are classified by twisted K-theory. Yet twisted K-theory is often hard to calculate. We argue that, in the case of a compactification on a simply-connected six manifold, twisted K-theory is isomorphic to a much simpler object, twisted homology. Unlike K-theory, homology can be twisted by a class of any degree and so it classifies not only D-branes but also M-branes. Twisted homology cl...

In this paper, we develop twisted K-theory for stacks, where the twisted class is given by an S-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure K α ⊗K j β → K i+j α+β are derived. Our approach provides a uniform framework for studying various twisted K-theories including the usual twisted K-theory of topological spaces...