Pimsner algebras and circle bundles

We report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with the examples of quantum weighted projective and lens spaces and theta-deformations.Comment: 24 pages. v3: Updated title. No changes in the scientific content and result

Pimsner algebras and Gysin sequences from principal circle actions

A self Morita equivalence over an algebra B, given by a B-bimodule E, is thought of as a line bundle over B. The corresponding Pimsner algebra O_E is then the total space algebra of a noncommutative principal circle bundle over B. A natural Gysin-like sequence relates the KK-theories of O_E and of B. Interesting examples come from O_E a quantum lens space over B a quantum weighted projective line (with arbitrary weights). The KK-theory of these spaces is explicitly computed and natural generators are exhibited.Comment: 29 pages. v2: Scientific content unchanged. Exposition improved. Added references. To appear in the JNc

The Gysin Sequence for Quantum Lens Spaces

We define quantum lens spaces as `direct sums of line bundles' and exhibit them as `total spaces' of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as `line bundles' over quantum lens spaces and generically define `torsion classes'. We work out explicit examples of these classes.Comment: 27 pages. v2: No changes in the scientific content and results. Section 5 completely re-written and a final section added; suppressed two appendices; added references; minor changes throughout the paper. To appear in the JNc

Quantum lattice gauge fields and groupoid C*-algebras

We present an operator-algebraic approach to the quantization and reduction of lattice field theories. Our approach uses groupoid C*-algebras to describe the observables and exploits Rieffel induction to implement the quantum gauge symmetries. We introduce direct systems of Hilbert spaces and direct systems of (observable) C*-algebras, and, dually, corresponding inverse systems of configuration spaces and (pair) groupoids. The continuum and thermodynamic limit of the theory can then be described by taking the corresponding limits, thereby keeping the duality between the Hilbert space and observable C*-algebra on the one hand, and the configuration space and the pair groupoid on the other. Since all constructions are equivariant with respect to the gauge group, the reduction procedure applies in the limit as well.Comment: 23 pages, 6 figure

In-vivo effects of flapless osteopuncture-facilitated tooth movement in the maxilla and the mandible

This study aimed to investigate the effects of a minimally invasive, flapless procedure to enhance tooth movement in both jaws and to determine whether this triggers the acceleration when repeated monthly. The sample consisted of thirty-two individuals whose orthodontic treatment required canine retraction. They were divided into an experimental group and control group. Osteopunctures were performed using orthodontic mini-screws at the distal aspects of the canine teeth at the beginning and on the fourth week of distalization in the experimental group. The control group was treated with conventional mechanics. All canines were retracted. The rates of canine distalization, rotation, and tipping were measured on the first, fourth, and eighth weeks of distalization. First molar anchorage loss was also measured. Intergroup and intragroup analyses were performed. Flapless osteopuncture-facilitated tooth movement resulted in greater canine distalization and reduced molar movement in the maxilla in the experimental than in the control group during the first month of distalization. In addition, the extent of upper canine movement was significantly higher in the experimental group in the first month than in the second. No differences in canine and molar movement in the mandible were observed between the two groups. OP, as applied in this study, is an effective method for increasing the rate of tooth movement in the maxilla. Repeating the procedure monthly does not appear to show a major advance of tooth movement

Through the Looking Glass: An Analysis of the Portrayals of Child Soldiers through the Lenses of Community Members and Key Stakeholders

This thesis explores the construction and deployment of global representations of child soldiers. The main argument is that understanding the representation of child soldiers by unravelling the way it is constructed has an important impact on policy applications when addressing child soldiers. In broadening the theoretical, conceptual and practical interpretations of the concept of ‘child soldier’, this thesis demonstrates some of the political effects of these portrayals. Given the multidimensional and multifaceted nature of the child soldier phenomenon, a cross-disciplinary approach is employed. Considering the relationship context in which child soldiers exist, this thesis argues that the child soldiers’ identity is a complex one that cannot be considered in isolation from the external stakeholders who contribute to its creation. Nor can the representation of child soldiers be dissociated from environmental, structural and cultural factors. Politically and materially, the identity ‘child soldier’ carries a range of meanings and implications in the process of post-war rehabilitation and reintegration of child ex-combatants into society. In these contexts, new meanings of childhood and of youth as a political identity emerge — meanings influenced by international discourse around children’s rights. The main hypothesis of my thesis is that the representation of child soldiers cannot escape the institutional, political and social positioning of the stakeholders. It is not possible to represent or act from the ‘outside’, since everyone is always already situated inside discourse, culture, institutions and geopolitics. Consequently, portrayals are always mediated by a confluence of diverse institutional interests and other identifiable externalities; in this regard, representation serves a utilitarian purpose

Principal circle bundles, Pimsner algebras and Gysin sequences

Principal circle bundles and Gysin sequences play a crucial role in mathematical physics, in particular in Chern-Simons theories and T-duality. This works focuses on the noncommutative topology of principal circle bundles: we investigate the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. At the C*-algebraic level, we start from a self-Morita equivalence bimodule E for a C*-algebra B which we think of as a non commutative line bundle over the `base space\u2019 algebra B. The corresponding Pimsner algebra O_E, is then the total space algebra of an associated circle bundle. A natural six term exact sequence, an analogue of the Gysin sequence for circle bundles, relates the KK-theories of O_E and of the base space B. We illustrate several results with the examples of quantum weighted projective and lens spaces