A manifold structure for the group of orbifold diffeomorphisms of a smooth orbifold

For a compact, smooth C^r orbifold (without boundary), we show that the topological structure of the orbifold diffeomorphism group is a Banach manifold for finite r \ge 1 and a Frechet manifold if r=infty. In each case, the local model is the separable Banach (Frechet) space of C^r (C^infty, resp.) orbisections of the tangent orbibundle.Comment: 26 pages, 2 figures, final versio

On the notions of suborbifold and orbifold embedding

The purpose of this article is to investigate the relationship between suborbifolds and orbifold embeddings. In particular, we give natural definitions of the notion of suborbifold and orbifold embedding and provide many examples. Surprisingly, we show that there are (topologically embedded) smooth suborbifolds which do not arise as the image of a smooth orbifold embedding. We are also able to characterize those suborbifolds which can arise as the images of orbifold embeddings. As an application, we show that a length-minimizing curve (a geodesic segment) in a Riemannian orbifold can always be realized as the image of an orbifold embedding.Comment: 11 pages. Final Version. arXiv admin note: text overlap with arXiv:1205.115

Elementary orbifold differential topology

Taking an elementary and straightforward approach, we develop the concept of a regular value for a smooth map f:O→P between smooth orbifolds O and P. We show that Sardʼs theorem holds and that the inverse image of a regular value is a smooth full suborbifold of O. We also study some constraints that the existence of a smooth orbifold map imposes on local isotropy groups. As an application, we prove a Borsuk no retraction theorem for compact orbifolds with boundary and some obstructions to the existence of real-valued orbifold maps from local model orbifold charts

Resilience Management: A Framework for Assessing and Improving the Resilience of Organisations

Resilient Organisations Research Report 2007/01Organisations today are increasingly aware of the need to prepare for the unexpected. High profile international events of the last decade, such as the September 11th terrorist attacks, the Indian Ocean tsunami, Hurricane Katrina and the emerging threat of a pandemic all serve to remind organisations that the unimaginable can and does happen. Stories emerge from these events of organisations that survived or failed; at first glance there does not appear to be a particular pattern. Some survivors had excellent disaster response plans in place; others had none, surviving purely on the merits of strong leadership and the commitment and determination of staff. Many organisations that are devastated simply never reopen again; others evolve so radically that they are hard to recognise from their pre-crisis form. This research project seeks to explore what it is that makes some organisations more able to survive a major crisis than others, and suggests a framework for both evaluating and improving the resilience of individual organisations

Ultraviolet Detection of the Binary Companion to the Type IIb SN 2001ig

We present HST/WFC3 ultraviolet imaging in the F275W and F336W bands of the Type IIb SN 2001ig at an age of more than 14 years. A clear point source is detected at the site of the explosion having $m_{\rm F275W}=25.39 \pm 0.10$ and $m_{\rm F336W}=25.88 \pm 0.13$ mag. Despite weak constraints on both the distance to the host galaxy NGC 7424 and the line-of-sight reddening to the supernova, this source matches the characteristics of an early B-type main sequence star having $19,000 < T_{\rm eff} < 22,000$ K and $\log (L_{\rm bol}/L_{\odot})=3.92 \pm 0.14$. A BPASS v2.1 binary evolution model, with primary and secondary masses of 13 M$_{\odot}$ and 9 M$_{\odot}$ respectively, is found to resemble simultaneously in the Hertzsprung-Russell diagram both the observed location of this surviving companion, and the primary star evolutionary endpoints for other Type IIb supernovae. This same model exhibits highly variable late-stage mass loss, as expected from the behavior of the radio light curves. A Gemini/GMOS optical spectrum at an age of 6 years reveals a narrow He II emission line, indicative of continuing interaction with a dense circumstellar medium at large radii from the progenitor. We review our findings on SN 2001ig in the context of binary evolution channels for stripped-envelope supernovae. Owing to the uncrowded nature of its environment in the ultraviolet, this study of SN 2001ig represents one of the cleanest detections to date of a surviving binary companion to a Type IIb supernova.Comment: 8 pages, 3 figures. Resubmitted to ApJ after minor changes requested by refere

The classification of frequencies in the {\gamma} Doradus / {\delta} Scuti hybrid star HD 49434

Hybrid stars of the {\gamma} Doradus and {\delta} Scuti pulsation types have great potential for asteroseismic analysis to explore their interior structure. To achieve this, mode identi- fications of pulsational frequencies observed in the stars must be made, a task which is far from simple. In this work we begin the analysis by scrutinizing the frequencies found in the CoRoT photometric satellite measurements and ground-based high-resolution spectroscopy of the hybrid star HD 49434. The results show almost no consistency between the frequencies found using the two techniques and no characteristic period spacings or couplings were identified in either dataset. The spectroscopic data additionally show no evidence for any long term (5 year) variation in the dominant frequency. The 31 spectroscopic frequencies identified have standard deviation profiles suggesting multiple modes sharing (l, m) in the {\delta} Scuti frequency region and several skewed modes sharing the same (l, m) in the {\gamma} Doradus frequency region. In addition, there is a clear frequency in the {\gamma} Doradus frequency region that appears to be unrelated to the others. We conclude HD 49434 remains a {\delta} Scuti/ {\gamma} Doradus candidate hybrid star but more sophisticated models dealing with rotation are sought to obtain a clear picture of the pulsational behaviour of this star.Comment: Accepted for publication in MNRAS December 201

The Stratified Structure of Spaces of Smooth Orbifold Mappings

We consider four notions of maps between smooth C^r orbifolds O, P with O compact (without boundary). We show that one of these notions is natural and necessary in order to uniquely define the notion of orbibundle pullback. For the notion of complete orbifold map, we show that the corresponding set of C^r maps between O and P with the C^r topology carries the structure of a smooth C^\infty Banach (r finite)/Frechet (r=infty) manifold. For the notion of complete reduced orbifold map, the corresponding set of C^r maps between O and P with the C^r topology carries the structure of a smooth C^\infty Banach (r finite)/Frechet (r=infty) orbifold. The remaining two notions carry a stratified structure: The C^r orbifold maps between O and P is locally a stratified space with strata modeled on smooth C^\infty Banach (r finite)/Frechet (r=infty) manifolds while the set of C^r reduced orbifold maps between O and P locally has the structure of a stratified space with strata modeled on smooth C^\infty Banach (r finite)/Frechet (r=infty) orbifolds. Furthermore, we give the explicit relationship between these notions of orbifold map. Applying our results to the special case of orbifold diffeomorphism groups, we show they inherit the structure of C^\infty Banach (r finite)/Frechet (r=infty) manifolds. In fact, for r finite they are topological groups, and for r=infty they are convenient Frechet Lie groups.Comment: 31 pages, 2 figures; corrected and expande

Spectroscopic Pulsational Frequency Identification and Mode Determination of Gamma Doradus Star HD135825

We present the mode identification of frequencies found in spectroscopic observations of the Gamma Doradus star HD135825. Four frequencies were successfully identified: 1.3150 +/- 0.0003 1/d; 0.2902 +/- 0.0004 1/d; 1.4045 +/- 0.0005 1/d; and 1.8829 +/- 0.0005 1/d. These correspond to (l, m) modes of (1,1), (2,-2), (4,0) and (1,1) respectively. Additional frequencies were found but they were below the signal-to-noise limit of the Fourier spectrum and not suitable for mode identification. The rotational axis inclination and vsini of the star were determined to be 87 degrees (nearly edge-on) and 39.7 km/s (moderate for Gamma Doradus stars) respectively. A simultaneous fit of these four modes to the line profile variations in the data gives a reduced chi square of 12.7. We confirm, based on the frequencies found, that HD135825 is a bona fide Gamma Doradus star.Comment: Accepted to MNRAS 2012 March