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Full-Text Articles in Science and Technology Studies
The Resolvent Cocycle In Twisted Cyclic Cohomology And A Local Index Formula For The Podle's Sphere, Adam Rennie, Roger Senior
The Resolvent Cocycle In Twisted Cyclic Cohomology And A Local Index Formula For The Podle's Sphere, Adam Rennie, Roger Senior
Associate Professor Adam Rennie
We continue the investigation of twisted homology theories in the context of dimension drop phenomena. This work unifies previous equivariant index calculations in twisted cyclic cohomology. We do this by proving the existence of the resolvent cocycle, a finitely summable analogue of the JLO cocycle, under weaker smoothness hypotheses and in the more general setting of 'modular' spectral triples. As an application we show that using our twisted resolvent cocycle, we can obtain a local index formula for the Podles sphere. The resulting twisted cyclic cocycle has non-vanishing Hochschild class which is in dimension 2.
Doing It Tough: Factors Impacting On Local E-Government Mmaturity, Peter Shackleton, Linda Dawson
Doing It Tough: Factors Impacting On Local E-Government Mmaturity, Peter Shackleton, Linda Dawson
Associate Professor Linda Dawson
As growing numbers of citizens seek to use the Internet to do business, governments across the world have moved into the area of electronic service delivery. For the last decade significant advancements have been made in the area of e-Government. Today, e-Government is often assumed to be wellestablished. However, ongoing support is often missing, particularly at the local government level. The multi-level nature of government often means that citizens are frustrated when accessing services that span many levels of bureaucracy. This paper describes an empirical study which explores the factors influencing local egovernment maturity and identifies the barriers, enablers, priorities …
The Local Index Formula In Noncommutative Geometry Revisited, Alan Carey, John Phillips, Adam Rennie, Fyodor Sukochev
The Local Index Formula In Noncommutative Geometry Revisited, Alan Carey, John Phillips, Adam Rennie, Fyodor Sukochev
Associate Professor Adam Rennie
In this review we discuss the local index formula in noncommutative geomety from the viewpoint of two new proofs are partly inspired by the approach of Higson especially that in but they differ in several fundamental aspedcts, in particular they apply to semifinite spectral triples for a *s-subalgebra A of a general semifinite von Neumann algebra. Our proofs are novel even in the setting of the original theorem and reduce the hypotheses of the theorem to those necessary for its statement. These proofs rely on the introduction of a function valued cocycle which is 'almost' a (b, B)-cocycle in the …
The Local Index Formula In Semifinite Von Neumann Algebras Ii: The Even Case, Alan Carey, John Phillips, Adam Rennie, F Sukochev
The Local Index Formula In Semifinite Von Neumann Algebras Ii: The Even Case, Alan Carey, John Phillips, Adam Rennie, F Sukochev
Associate Professor Adam Rennie
We generalise the even local index formula of Connes and Moscovici to the case of spectral triples for a ∗-subalgebra A of a general semifinite von Neumann algebra. The proof is a variant of that for the odd case which appears in Part I. To allow for algebras with a non-trivial centre we have to establish a theory of unbounded Fredholm operators in a general semifinite von Neumann algebra and in particular prove a generalised McKean-Singer formula.
The Local Index Formula In Semifinite Von Neumann Algebras I: Spectral Flow, Alan Carey, John Phillips, Adam Rennie, Fyodor Sukochev
The Local Index Formula In Semifinite Von Neumann Algebras I: Spectral Flow, Alan Carey, John Phillips, Adam Rennie, Fyodor Sukochev
Associate Professor Adam Rennie
We generalise the local index formula of Connes and Moscovici to the case of spectral triples for a ∗-subalgebra A of a general semifinite von Neumann algebra. In this setting it gives a formula for spectral flow along a path joining an unbounded self-adjoint Breuer-Fredholm operator, affiliated to the von Neumann algebra, to a unitarily equivalent operator. Our proof is novel even in the setting of the original theorem and relies on the introduction of a function valued cocycle which is 'almost' a (b,B)-cocycle in the cyclic cohomology of A.
Statistical Indicators For Local Government Areas: A Case Study Of The Shoalhaven Lga, 1997, Nell Stetner-Houweling, David Steel, Greg Pullen
Statistical Indicators For Local Government Areas: A Case Study Of The Shoalhaven Lga, 1997, Nell Stetner-Houweling, David Steel, Greg Pullen
Professor David Steel
Decision makers and planers need to have relevant and reliable information to give a picture of how different areas are developing economically and socially. However, there is a perceived lack of timely and easily accessible data at the Local Government Area (LGA) level. This study produced a statistical profile of the Shoalhaven (LGA) by developing a conceptual framework, which represents the key economic, social, and population characteristics of the LGA. The statistical data available from the Australian Bureau of Statistics (ABS) at the level of the LGA, was investigated and summarised. Other sources of information available to create a statistical …