Local Proof of Algebraic Characterization of Free Actions

Let G be a compact Hausdorff topological group acting on a compact Hausdorff topological space X. Within the C∗-algebra C(X) of all continuous complex-valued functions on X, there is the Peter-Weyl algebra PG(X) which is the (purely algebraic) direct sum of the isotypical components for the action of G on C(X). We prove that the action of G on X is free if and only if the canonical map PG(X)⊗C(X/G)PG(X)→PG(X)⊗O(G) is bijective. Here both tensor products are purely algebraic, and O(G) denotes the Hopf algebra of ''polynomial'' functions on G

On piecewise trivial Hopf—Galois extensions

We discuss a noncommutative generalization of compact principal bundles that can be trivialized relative to the finite covering by closed sets. In this setting we present bundle reconstruction and reduction

On localization in holomorphic equivariant cohomology

We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.Comment: 16 pages. Completely rewritten, new title. v3: Minor changes in the exposition. v4: final version to appear in Centr. Eur. J. Mat

Can black holes be torn up by phantom dark energy in cyclic cosmology?

Infinitely cyclic cosmology is often frustrated by the black hole problem. It has been speculated that this obstacle in cyclic cosmology can be removed by taking into account a peculiar cyclic model derived from loop quantum cosmology or the braneworld scenario, in which phantom dark energy plays a crucial role. In this peculiar cyclic model, the mechanism of solving the black hole problem is through tearing up black holes by phantom. However, using the theory of fluid accretion onto black holes, we show in this paper that there exists another possibility: that black holes cannot be torn up by phantom in this cyclic model. We discussed this possibility and showed that the masses of black holes might first decrease and then increase, through phantom accretion onto black holes in the expanding stage of the cyclic universe.Comment: 6 pages, 2 figures; discussions adde

Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom

We consider natural complex Hamiltonian systems with $n$ degrees of freedom given by a Hamiltonian function which is a sum of the standard kinetic energy and a homogeneous polynomial potential $V$ of degree $k>2$. The well known Morales-Ramis theorem gives the strongest known necessary conditions for the Liouville integrability of such systems. It states that for each $k$ there exists an explicitly known infinite set \scM_k\subset\Q such that if the system is integrable, then all eigenvalues of the Hessian matrix V''(\vd) calculated at a non-zero \vd\in\C^n satisfying V'(\vd)=\vd, belong to \scM_k. The aim of this paper is, among others, to sharpen this result. Under certain genericity assumption concerning $V$ we prove the following fact. For each $k$ and $n$ there exists a finite set \scI_{n,k}\subset\scM_k such that if the system is integrable, then all eigenvalues of the Hessian matrix V''(\vd) belong to \scI_{n,k}. We give an algorithm which allows to find sets \scI_{n,k}. We applied this results for the case $n=k=3$ and we found all integrable potentials satisfying the genericity assumption. Among them several are new and they are integrable in a highly non-trivial way. We found three potentials for which the additional first integrals are of degree 4 and 6 with respect to the momenta.Comment: 54 pages, 1 figur

Dark Energy and Gravity

I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as the candidate and emphasises why no other approach really solves the conceptual problems usually attributed to the cosmological constant. Part 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract the key ingredients which must be present in any viable solution. I argue that (i)the cosmological constant problem cannot be satisfactorily solved until gravitational action is made invariant under the shift of the matter lagrangian by a constant and (ii) this cannot happen if the metric is the dynamical variable. Hence the cosmological constant problem essentially has to do with our (mis)understanding of the nature of gravity. Part 3 discusses an alternative perspective on gravity in which the action is explicitly invariant under the above transformation. Extremizing this action leads to an equation determining the background geometry which gives Einstein's theory at the lowest order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy, edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure

Skills and training in the hotel sector: The case of front office employment in Northern Ireland

Notwithstanding the globalisation of services and the migration of some service providers (call centres, financial processing) to regions of low cost labour coupled with high levels of education attainment, there are arguments that the skills, which employees bring to the workplace in executing common tasks, are context and culture specific. This paper is concerned with the skills set and training background of one set of service workers, those in hotel front office, located within Northern Ireland. This paper reports the findings of a survey of front office workers working in 4- and 5-star hotels in Northern Ireland. This survey identifies the skills and training profile of this group of employees and measures attitudes to key skills requirements within front office work

Cultural diversity

Aimed at undergraduate students in Ireland who are studying for hospitality degrees, Hospitality Management in Ireland: Theory and Practice is responding to an upsurge of interest in the area of hospitality and tourism. Explores the importance of human resource management, training and development, employee relations, and cultural diversity to the industry's development

Place, people and interpretation: issues of migrant labour and tourism imagery in Ireland

This paper addresses the contribution of tourism's workforce to destination image and branding and considers the role that employees play in visitors' interpretation of their experience of place. The focus of this paper is on the contribution of working people to the image of place and the potential for contradiction in imagery as the people who inhabit and work within a place change over time. At the same time, those consuming the place as visitors may well have expectations that are fixed in traditional and outdated imagery. The location of this paper is Ireland where the traditional marketing of the tourism brand has given core roles to images of people and the friendliness of Irish hospitality, represented by traditional and homogeneous images. Interpretation of Ireland as a destination, in the tourist literature, by tour guides and within the cultural heritage sector generally, has widely perpetuated these traditional and, arguably, clichéd images. Recent growth in the "Celtic tiger" economy has induced unprecedented and large scale migration from countries across the globe to Ireland, particularly into the tourism sector. This paper raises questions with regard to interpretation and branding of a country as a tourist destination in the light of major changes within the demography and ethnicity of its tourism workforce

Cultural Diversity in Hospitality Work: The Northern Ireland Experience

International workers are a growing category of employees in the hospitality industry of Northern Ireland (NI). The retention and skills shortages of the industry are significant factors in facilitating this increase. Thus, international workers could be an invaluable new source of labour for the hospitality industry, provided that they are properly looked after and managed. However, little is known about the number of people moving to Northern Ireland to take up work in the hospitality industry. This paper sets out to answer some of the 'unknowns' - including nationality, demographic characteristics, educational, employment and economic background. The paper draws on data collected through a survey of migrant workers in nine hotels in Northern Ireland and focus groups with migrant employees in all of the survey establishments. Issues of social integration within the workforce and the wider community as well as the future that migrant workers see for themselves are discussed from a human resource perspective