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Item Restricted Topology and Flux of T-Dual Manifolds with Circle Actions(Springer, 2012) Varghese, M.; Wu, S.We present an explicit formula for the topology and H-flux of the T-dual of a general type II, compactification, significantly generalizing earlier results. Our results apply to T-dualities with respect to any circle action on spacetime X. As before, T-duality exchanges type IIA and type IIB string theories. A new consequence is that the T-dual spacetime is a singular space when the fixed point set XT is non-empty; the singularities correspond to Kaluza-Klein monopoles. We propose that the Ramond-Ramond charges of type II string theories on the singular dual are classified by twisted equivariant cohomology groups. We also discuss the K-theory approach.Item Metadata only Co-morbidity and the utilization of health care for Australian veterans with diabetes(Blackwell Publishing Ltd, 2010) Zhang, Y.; Vitry, A.; Roughead, E.; Ryan, P.; Gilbert, A.Objective To examine the impact of co-morbidity on health service utilization by Australian veterans with diabetes. Methods A retrospective cohort study was undertaken including veterans aged ≥ 65 years dispensed medicines for diabetes in 2006. Data were sourced from the Australian Department of Veterans’ Affairs health claims database. Utilization of preventive health services for diabetes was assessed, including claims for glycated haemoglobin (HbA1c) test, microabuminuria, podiatry services, diabetes care plans, medication reviews, case conferences, general practitioner (GP) management plans and ophthalmology/optometry services. Results Among the 17 095 veterans dispensed medicines for diabetes, more than 80% had four or more co-morbid conditions. Those with a higher number of co-morbidities were more likely to have had claims for optometry/ophthalmology services and podiatry services, but not for other services. Veterans with at least one diabetes-related hospital admission had no more claims for diabetes health services than those who had no diabetics-related hospital admission, except for endocrinology services (relative risk = 1.26, 95% confidence intervals 1.15–1.37). Veterans with dementia were less likely to have had claims for diabetes health services while patients with renal failure were more likely to have had claims for the services. Conclusions Low utilization of preventive diabetes care services is apparent in all co-morbidity groups. Patients with renal failure or dementia used more and less health services resources, respectively. Given the high mean age of this population, there may be valid reasons for the low use, such as competing health demands and patients’ preferences.Item Open Access The index of projective families of elliptic operators: the decomposable case(Soc Mathematique France, 2009) Varghese, M.; Melrose, R.; Singer, I.An index theory for projective families of elliptic pseudodifferential operators is developed under two conditions. First, that the twisting, i.e. Dixmier-Douady, class is in H2(X; Z)[H1(X; Z) H3(X; Z) and secondly that the 2-class part is trivialized on the total space of the fibration. One of the features of this special case is that the corresponding Azumaya bundle can be refined to a bundle of smoothing operators. The topological and the analytic index of a projective family of elliptic operators associated with the smooth Azumaya bundle both take values in twisted K-theory of the parameterizing space and the main result is the equality of these two notions of index. The twisted Chern character of the index class is then computed by a variant of Chern-Weil theory.Item Metadata only D-branes, KK-theory and duality on noncommutative spaces(Institute of Physics Publishing, 2008) Brodzki, J.; Varghese, M.; Rosenberg, J.; Szabo, R.; International Conference on Non-commutative Geometry and Physics (23 Apr 2007 - 27 Apr 2007 : Orsay, France)We present a new categorical classification framework for D-brane charges on noncommutative manifolds using methods of bivariant K-theory. We describe several applications including an explicit formula for D-brane charge in cyclic homology, a realignement of open string T-duality, and a general criterion for cancellation of global worldsheet anomalies.Item Metadata only Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras(Elsevier Science BV, 2007) Eastwood, Michael George; Somberg, Petr; Soucek, Vladimir; School of Mathematical Sciences : Pure MathematicsUsing deformation theory, Braverman and Joseph constructed certain primitive ideals in the enveloping algebras of the simple Lie algebras. Except in the case , there is a special value of the deformation parameter giving an ideal of infinite codimension. For the classical Lie algebras, the uniqueness of the special value is equivalent to the existence of tensors with very particular properties. The existence of these tensors was concluded abstractly by Braverman and Joseph but here we present explicit formulae. This allows a rather direct computation of the special value of the deformation parameter.Item Metadata only Euler characteristics and chromatic polynomials(Academic Press, 2007) Eastwood, Michael George; Huggett, Stephen; School of Mathematical Sciences : Pure MathematicsItem Metadata only D-Branes, RR-Fields and Duality on Noncommutative Manifolds(Springer, 2008) Brodzki, J.; Varghese, M.; Rosenberg, J.; Szabo, R.We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of T-duality as well as establishing a very general formula for D-brane charges. This formula is closely related to a noncommutative Grothendieck-Riemann-Roch theorem that is proved here. Our approach relies on a very general form of Poincaré duality, which is studied here in detail. Among the technical tools employed are calculations with iterated products in bivariant -theory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams.Item Metadata only Entire cyclic homology of stable continuous trace algebras(London Math Soc, 2007) Varghese, M.; Stevenson, D.A central result in this paper is the computation of the entire cyclic homology of canonical smooth subalgebras of stable continuous trace C*-algebras having smooth manifolds M as their spectrum. More precisely, the entire cyclic homology is shown to be canonically isomorphic to the continuous periodic cyclic homology for these algebras. By an earlier result of the authors, one concludes that the entire cyclic homology of the algebra is canonically isomorphic to the twisted de Rham cohomology of M.Item Metadata only Heat kernels and the range of the trace on completions of twisted group algebras(American Mathematical Society, 2006) Varghese, M.; Jorgenson, J.; Walling, L.Heat kernels are used in this paper to express the analytic index of projectively invariant Dirac type operators on G-covering spaces of compact manifolds, as elements in the K-theory of certain unconditional completions of the twisted group algebra of G. This is combined with V. Lafforgue's results in the untwisted case, to compute the range of the trace on the K-theory of these algebras, under the hypothesis that G is in the class C' (defined by V. Lafforgue).Item Metadata only Kato’s inequality for magnetic Laplacians on graphs(American Mathematical Society, 2006) Varghese, M.; Dodziuk, J.; AMS special session, the ubiquitous heat kernel, October 2-4, Boulder, Colorado (2 Apr 2003 : Boulder, Colorado, USA)Item Metadata only Approximating Spectral invariants of Harper operators on graphs II(Amer Mathematical Soc, 2003) Varghese, M.; Schick, T.; Yates, S.We study Harper operators and the closely related discrete magnetic Laplacians (DML) on a graph with a free action of a discrete group, as defined by Sunada. The spectral density function of the DML is defined using the von Neumann trace associated with the free action of a discrete group on a graph. The main result in this paper states that when the group is amenable, the spectral density function is equal to the integrated density of states of the DML that is defined using either Dirichlet or Neumann boundary conditions. This establishes the main conjecture in a paper by Mathai and Yates. The result is generalized to other self adjoint operators with finite propagation speed.Item Open Access Conjugate functions and semiconformal mappings(2004) Eastwood, Michael George; Baird, Paul; International Conference On Differential Geometry And Its Applications (9th : 2004 : Prague, Czech Republic); School of Mathematical Sciences : Pure MathematicsItem Metadata only Some special geometry in dimension six(2002) Eastwood, Michael George; Cap, A.; School of Mathematical Sciences : Pure MathematicsWe generalise the notion of contact manifold by allowing the contact distribution to have codimension two. There are special features in dimension six. In particular, we show that the complex structure on a three-dimensional complex contact manifold is determined solely by the underlying contact distribution.Item Metadata only The Hill-Penrose-Sparling C.R.-folds(Chapman & Hall / CRC, 2001) Eastwood, Michael George; School of Mathematical Sciences : Pure MathematicsItem Metadata only Superambitwistors(Chapman & Hall/CRC, 2001) Eastwood, Michael George; School of Mathematical Sciences : Pure MathematicsItem Metadata only Formal thickenings of ambitwistors for curved space-time(Chapman & Hall / CRC, 2001) Eastwood, Michael George; School of Mathematical Sciences : Pure MathematicsItem Metadata only Some remarks on non-Abelian sheaf cohomology(Chapman & Hall / CRC, 2001) Eastwood, Michael George; School of Mathematical Sciences : Pure MathematicsItem Metadata only Superstructure versus formal neighbourhoods(Chapman & Hall / CRC, 2001) Eastwood, Michael George; School of Mathematical Sciences : Pure MathematicsItem Metadata only Conformally invariant differential operators on spin bundles(Chapman & Hall / CRC, 2001) Eastwood, Michael George; School of Mathematical Sciences : Pure MathematicsItem Metadata only The Einstein bundle of a non-linear graviton(Chapman & Hall / CRC, 2001) Eastwood, Michael George; School of Mathematical Sciences : Pure Mathematics